ipopt_options.m

function opt = ipopt_options(overrides, mpopt)
%IPOPT_OPTIONS  Sets options for IPOPT.
%
%   OPT = IPOPT_OPTIONS
%   OPT = IPOPT_OPTIONS(OVERRIDES)
%   OPT = IPOPT_OPTIONS(OVERRIDES, FNAME)
%   OPT = IPOPT_OPTIONS(OVERRIDES, MPOPT)
%
%   Sets the values for the options.ipopt struct normally passed to
%   IPOPT.
%
%   Please note that if there is a file named 'ipopt.opt' in your
%   current working directory, it will override any options passed
%   to the IPOPT MEX file, including any options returned by this
%   function.
%
%   Inputs are all optional, second argument must be either a string
%   (FNAME) or a struct (MPOPT):
%
%       OVERRIDES - struct containing values to override the defaults
%       FNAME - name of user-supplied function called after default
%           options are set to modify them. Calling syntax is:
%                   MODIFIED_OPT = FNAME(DEFAULT_OPT);
%       MPOPT - MATPOWER options struct, uses the following fields:
%           opf.violation   - used to set opt.constr_viol_tol
%           verbose         - used to opt.print_level
%           ipopt.opts      - struct containing values to use as OVERRIDES
%           ipopt.opt_fname - name of user-supplied function used as FNAME,
%               except with calling syntax:
%                   MODIFIED_OPT = FNAME(DEFAULT_OPT, MPOPT);
%           ipopt.opt       - numbered user option function, if and only if
%               ipopt.opt_fname is empty and ipopt.opt is non-zero, the value
%               of ipopt.opt_fname is generated by appending ipopt.opt to
%               'ipopt_user_options_' (for backward compatibility with old
%               MATPOWER option IPOPT_OPT).
%
%   Output is an options.ipopt struct to pass to IPOPT.
%
%   There are multiple ways of providing values to override the default
%   options. Their precedence and order of application are as follows:
%
%   With inputs OVERRIDES and FNAME
%       1. FNAME is called
%       2. OVERRIDES are applied
%   With inputs OVERRIDES and MPOPT
%       1. FNAME (from ipopt.opt_fname or ipopt.opt) is called
%       2. ipopt.opts (if not empty) are applied
%       3. OVERRIDES are applied
%
%   Example:
%
%   If ipopt.opt = 3, then after setting the default IPOPT options,
%   IPOPT_OPTIONS will execute the following user-defined function
%   to allow option overrides:
%
%       opt = ipopt_user_options_3(opt, mpopt);
%
%   The contents of ipopt_user_options_3.m, could be something like:
%
%       function opt = ipopt_user_options_3(opt, mpopt)
%       opt.nlp_scaling_method = 'none';
%       opt.max_iter           = 500;
%       opt.derivative_test    = 'first-order';
%
%   See the options reference section in the IPOPT documentation for
%   details on the available options.
%
%       http://www.coin-or.org/Ipopt/documentation/
%
%   See also IPOPT, MPOPTION.

%   MATPOWER
%   Copyright (c) 2010-2016, Power Systems Engineering Research Center (PSERC)
%   by Ray Zimmerman, PSERC Cornell
%
%   This file is part of MATPOWER.
%   Covered by the 3-clause BSD License (see LICENSE file for details).
%   See http://www.pserc.cornell.edu/matpower/ for more info.

%%-----  initialization and arg handling  -----
%% defaults
verbose = 2;
fname   = '';

%% second argument
if nargin > 1 && ~isempty(mpopt)
    if ischar(mpopt)        %% 2nd arg is FNAME (string)
        fname = mpopt;
        have_mpopt = 0;
    else                    %% 2nd arg is MPOPT (MATPOWER options struct)
        have_mpopt = 1;
        verbose = mpopt.verbose;
        if isfield(mpopt.ipopt, 'opt_fname') && ~isempty(mpopt.ipopt.opt_fname)
            fname = mpopt.ipopt.opt_fname;
        elseif mpopt.ipopt.opt
            fname = sprintf('ipopt_user_options_%d', mpopt.ipopt.opt);
        end
    end
else
    have_mpopt = 0;
end

%%-----  set default options for IPOPT  -----
%% printing
if verbose
    opt.print_level = min(12, verbose*2+1);
else
    opt.print_level = 0;
end

%% convergence
opt.tol             = 1e-8;                 %% default 1e-8
opt.max_iter        = 250;                  %% default 3000
opt.dual_inf_tol    = 0.1;                  %% default 1
if have_mpopt
    opt.constr_viol_tol = mpopt.opf.violation;                  %% default 1e-4
    opt.acceptable_constr_viol_tol = mpopt.opf.violation*100;   %% default 1e-2
end
opt.compl_inf_tol   = 1e-5;                 %% default 1e-4
opt.acceptable_tol  = 1e-8;                 %% default 1e-6
% opt.acceptable_iter = 15;                   %% default 15
% opt.acceptable_dual_inf_tol     = 1e+10;    %% default 1e+10
opt.acceptable_compl_inf_tol    = 1e-3;     %% default 1e-2
% opt.acceptable_obj_change_tol   = 1e+20;    %% default 1e+20
% opt.diverging_iterates_tol      = 1e+20;    %% default 1e+20

%% NLP scaling
% opt.nlp_scaling_method  = 'none';           %% default 'gradient-based'

%% NLP
% opt.fixed_variable_treatment    = 'make_constraint';    %% default 'make_parameter'
% opt.honor_original_bounds       = 'no';                 %% default 'yes'
% opt.check_derivatives_for_naninf = 'yes';               %% default 'no'

%% initialization
% opt.least_square_init_primal    = 'yes';        %% default 'no'
% opt.least_square_init_duals     = 'yes';        %% default 'no'

%% barrier parameter update
opt.mu_strategy                 = 'adaptive';   %% default 'monotone'

%% linear solver
% opt.linear_solver   = 'ma27';
% opt.linear_solver   = 'ma57';
% opt.linear_solver   = 'pardiso';
% opt.linear_solver   = 'wsmp';
% opt.linear_solver   = 'mumps';          %% default 'mumps'
% opt.linear_solver   = 'custom';
% opt.linear_scaling_on_demand    = 'no'; %% default 'yes'

%% step calculation
% opt.mehrotra_algorithm      = 'yes';    %% default 'no'
% opt.fast_step_computation   = 'yes';    %% default 'no'

%% restoration phase
% opt.expect_infeasible_problem   = 'yes';    %% default 'no'

%% derivative checker
% opt.derivative_test         = 'second-order';   %% default 'none'

%% hessian approximation
% opt.hessian_approximation   = 'limited-memory'; %% default 'exact'

% ma57 options
%opt.ma57_pre_alloc = 3;
%opt.ma57_pivot_order = 4;

%%-----  call user function to modify defaults  -----
if ~isempty(fname)
    if have_mpopt
        opt = feval(fname, opt, mpopt);
    else
        opt = feval(fname, opt);
    end
end

%%-----  apply overrides  -----
if have_mpopt && isfield(mpopt.ipopt, 'opts') && ~isempty(mpopt.ipopt.opts)
    opt = nested_struct_copy(opt, mpopt.ipopt.opts);
end
if nargin > 0 && ~isempty(overrides)
    opt = nested_struct_copy(opt, overrides);
end


%--------------------------  Options Documentation  --------------------------
% (as printed by IPOPT 3.8)
% ### Output ###
% 
% print_level                            0 <= (          5) <= 12        
%    Output verbosity level.
%      Sets the default verbosity level for console output. The larger this
%      value the more detailed is the output.
% 
% output_file                   ("")
%    File name of desired output file (leave unset for no file output).
%      NOTE: This option only works when read from the ipopt.opt options file!
%      An output file with this name will be written (leave unset for no file
%      output).  The verbosity level is by default set to "print_level", but can
%      be overridden with "file_print_level".  The file name is changed to use
%      only small letters.
%    Possible values:
%     - *                       [Any acceptable standard file name]
% 
% file_print_level                       0 <= (          5) <= 12        
%    Verbosity level for output file.
%      NOTE: This option only works when read from the ipopt.opt options file!
%      Determines the verbosity level for the file specified by "output_file". 
%      By default it is the same as "print_level".
% 
% print_user_options            ("no")
%    Print all options set by the user.
%      If selected, the algorithm will print the list of all options set by the
%      user including their values and whether they have been used.  In some
%      cases this information might be incorrect, due to the internal program
%      flow.
%    Possible values:
%     - no                      [don't print options]
%     - yes                     [print options]
% 
% print_options_documentation   ("no")
%    Switch to print all algorithmic options.
%      If selected, the algorithm will print the list of all available
%      algorithmic options with some documentation before solving the
%      optimization problem.
%    Possible values:
%     - no                      [don't print list]
%     - yes                     [print list]
% 
% print_timing_statistics       ("no")
%    Switch to print timing statistics.
%      If selected, the program will print the CPU usage (user time) for
%      selected tasks.
%    Possible values:
%     - no                      [don't print statistics]
%     - yes                     [print all timing statistics]
% 
% option_file_name              ("")
%    File name of options file (to overwrite default).
%      By default, the name of the Ipopt options file is "ipopt.opt" - or
%      something else if specified in the IpoptApplication::Initialize call. If
%      this option is set by SetStringValue BEFORE the options file is read, it
%      specifies the name of the options file.  It does not make any sense to
%      specify this option within the options file.
%    Possible values:
%     - *                       [Any acceptable standard file name]
% 
% replace_bounds                ("no")
%    Indicates if all variable bounds should be replaced by inequality
%    constraints
%      This option must be set for the inexact algorithm
%    Possible values:
%     - no                      [leave bounds on variables]
%     - yes                     [replace variable bounds by inequality
%                                constraints]
% 
% skip_finalize_solution_call   ("no")
%    Indicates if call to NLP::FinalizeSolution after optimization should be
%    suppressed
%      In some Ipopt applications, the user might want to call the
%      FinalizeSolution method separately.  Setting this option to "yes" will
%      cause the IpoptApplication object to suppress the default call to that
%      method.
%    Possible values:
%     - no                      [call FinalizeSolution]
%     - yes                     [do not call FinalizeSolution]
% 
% print_info_string             ("no")
%    Enables printing of additional info string at end of iteration output.
%      This string contains some insider information about the current iteration.
%    Possible values:
%     - no                      [don't print string]
%     - yes                     [print string at end of each iteration output]
% 
% 
% 
% ### Convergence ###
% 
% tol                                    0 <  (      1e-08) <  +inf      
%    Desired convergence tolerance (relative).
%      Determines the convergence tolerance for the algorithm.  The algorithm
%      terminates successfully, if the (scaled) NLP error becomes smaller than
%      this value, and if the (absolute) criteria according to "dual_inf_tol",
%      "primal_inf_tol", and "cmpl_inf_tol" are met.  (This is epsilon_tol in
%      Eqn. (6) in implementation paper).  See also "acceptable_tol" as a second
%      termination criterion.  Note, some other algorithmic features also use
%      this quantity to determine thresholds etc.
% 
% s_max                                  0 <  (        100) <  +inf      
%    Scaling threshold for the NLP error.
%      (See paragraph after Eqn. (6) in the implementation paper.)
% 
% max_iter                               0 <= (       3000) <  +inf      
%    Maximum number of iterations.
%      The algorithm terminates with an error message if the number of
%      iterations exceeded this number.
% 
% max_cpu_time                           0 <  (      1e+06) <  +inf      
%    Maximum number of CPU seconds.
%      A limit on CPU seconds that Ipopt can use to solve one problem.  If
%      during the convergence check this limit is exceeded, Ipopt will terminate
%      with a corresponding error message.
% 
% dual_inf_tol                           0 <  (          1) <  +inf      
%    Desired threshold for the dual infeasibility.
%      Absolute tolerance on the dual infeasibility. Successful termination
%      requires that the max-norm of the (unscaled) dual infeasibility is less
%      than this threshold.
% 
% constr_viol_tol                        0 <  (     0.0001) <  +inf      
%    Desired threshold for the constraint violation.
%      Absolute tolerance on the constraint violation. Successful termination
%      requires that the max-norm of the (unscaled) constraint violation is less
%      than this threshold.
% 
% compl_inf_tol                          0 <  (     0.0001) <  +inf      
%    Desired threshold for the complementarity conditions.
%      Absolute tolerance on the complementarity. Successful termination
%      requires that the max-norm of the (unscaled) complementarity is less than
%      this threshold.
% 
% acceptable_tol                         0 <  (      1e-06) <  +inf      
%    "Acceptable" convergence tolerance (relative).
%      Determines which (scaled) overall optimality error is considered to be
%      "acceptable." There are two levels of termination criteria.  If the usual
%      "desired" tolerances (see tol, dual_inf_tol etc) are satisfied at an
%      iteration, the algorithm immediately terminates with a success message. 
%      On the other hand, if the algorithm encounters "acceptable_iter" many
%      iterations in a row that are considered "acceptable", it will terminate
%      before the desired convergence tolerance is met. This is useful in cases
%      where the algorithm might not be able to achieve the "desired" level of
%      accuracy.
% 
% acceptable_iter                        0 <= (         15) <  +inf      
%    Number of "acceptable" iterates before triggering termination.
%      If the algorithm encounters this many successive "acceptable" iterates
%      (see "acceptable_tol"), it terminates, assuming that the problem has been
%      solved to best possible accuracy given round-off.  If it is set to zero,
%      this heuristic is disabled.
% 
% acceptable_dual_inf_tol                0 <  (      1e+10) <  +inf      
%    "Acceptance" threshold for the dual infeasibility.
%      Absolute tolerance on the dual infeasibility. "Acceptable" termination
%      requires that the (max-norm of the unscaled) dual infeasibility is less
%      than this threshold; see also acceptable_tol.
% 
% acceptable_constr_viol_tol             0 <  (       0.01) <  +inf      
%    "Acceptance" threshold for the constraint violation.
%      Absolute tolerance on the constraint violation. "Acceptable" termination
%      requires that the max-norm of the (unscaled) constraint violation is less
%      than this threshold; see also acceptable_tol.
% 
% acceptable_compl_inf_tol               0 <  (       0.01) <  +inf      
%    "Acceptance" threshold for the complementarity conditions.
%      Absolute tolerance on the complementarity. "Acceptable" termination
%      requires that the max-norm of the (unscaled) complementarity is less than
%      this threshold; see also acceptable_tol.
% 
% acceptable_obj_change_tol              0 <= (      1e+20) <  +inf      
%    "Acceptance" stopping criterion based on objective function change.
%      If the relative change of the objective function (scaled by
%      Max(1,|f(x)|)) is less than this value, this part of the acceptable
%      tolerance termination is satisfied; see also acceptable_tol.  This is
%      useful for the quasi-Newton option, which has trouble to bring down the
%      dual infeasibility.
% 
% diverging_iterates_tol                 0 <  (      1e+20) <  +inf      
%    Threshold for maximal value of primal iterates.
%      If any component of the primal iterates exceeded this value (in absolute
%      terms), the optimization is aborted with the exit message that the
%      iterates seem to be diverging.
% 
% 
% 
% ### NLP Scaling ###
% 
% nlp_scaling_method            ("gradient-based")
%    Select the technique used for scaling the NLP.
%      Selects the technique used for scaling the problem internally before it
%      is solved. For user-scaling, the parameters come from the NLP. If you are
%      using AMPL, they can be specified through suffixes ("scaling_factor")
%    Possible values:
%     - none                    [no problem scaling will be performed]
%     - user-scaling            [scaling parameters will come from the user]
%     - gradient-based          [scale the problem so the maximum gradient at
%                                the starting point is scaling_max_gradient]
%     - equilibration-based     [scale the problem so that first derivatives are
%                                of order 1 at random points (only available
%                                with MC19)]
% 
% obj_scaling_factor                  -inf <  (          1) <  +inf      
%    Scaling factor for the objective function.
%      This option sets a scaling factor for the objective function. The scaling
%      is seen internally by Ipopt but the unscaled objective is reported in the
%      console output. If additional scaling parameters are computed (e.g.
%      user-scaling or gradient-based), both factors are multiplied. If this
%      value is chosen to be negative, Ipopt will maximize the objective
%      function instead of minimizing it.
% 
% nlp_scaling_max_gradient               0 <  (        100) <  +inf      
%    Maximum gradient after NLP scaling.
%      This is the gradient scaling cut-off. If the maximum gradient is above
%      this value, then gradient based scaling will be performed. Scaling
%      parameters are calculated to scale the maximum gradient back to this
%      value. (This is g_max in Section 3.8 of the implementation paper.) Note:
%      This option is only used if "nlp_scaling_method" is chosen as
%      "gradient-based".
% 
% nlp_scaling_obj_target_gradient         0 <= (          0) <  +inf      
%    Target value for objective function gradient size.
%      If a positive number is chosen, the scaling factor the objective function
%      is computed so that the gradient has the max norm of the given size at
%      the starting point.  This overrides nlp_scaling_max_gradient for the
%      objective function.
% 
% nlp_scaling_constr_target_gradient         0 <= (          0) <  +inf      
%    Target value for constraint function gradient size.
%      If a positive number is chosen, the scaling factor the constraint
%      functions is computed so that the gradient has the max norm of the given
%      size at the starting point.  This overrides nlp_scaling_max_gradient for
%      the constraint functions.
% 
% 
% 
% ### NLP ###
% 
% nlp_lower_bound_inf                 -inf <  (     -1e+19) <  +inf      
%    any bound less or equal this value will be considered -inf (i.e. not lower
%    bounded).
% 
% nlp_upper_bound_inf                 -inf <  (      1e+19) <  +inf      
%    any bound greater or this value will be considered +inf (i.e. not upper
%    bounded).
% 
% fixed_variable_treatment      ("make_parameter")
%    Determines how fixed variables should be handled.
%      The main difference between those options is that the starting point in
%      the "make_constraint" case still has the fixed variables at their given
%      values, whereas in the case "make_parameter" the functions are always
%      evaluated with the fixed values for those variables.  Also, for
%      "relax_bounds", the fixing bound constraints are relaxed (according to"
%      bound_relax_factor"). For both "make_constraints" and "relax_bounds",
%      bound multipliers are computed for the fixed variables.
%    Possible values:
%     - make_parameter          [Remove fixed variable from optimization
%                                variables]
%     - make_constraint         [Add equality constraints fixing variables]
%     - relax_bounds            [Relax fixing bound constraints]
% 
% dependency_detector           ("none")
%    Indicates which linear solver should be used to detect linearly dependent
%    equality constraints.
%      The default and available choices depend on how Ipopt has been compiled. 
%      This is experimental and does not work well.
%    Possible values:
%     - none                    [don't check; no extra work at beginning]
%     - mumps                   [use MUMPS]
%     - wsmp                    [use WSMP]
%     - ma28                    [use MA28]
% 
% dependency_detection_with_rhs ("no")
%    Indicates if the right hand sides of the constraints should be considered
%    during dependency detection
%    Possible values:
%     - no                      [only look at gradients]
%     - yes                     [also consider right hand side]
% 
% num_linear_variables                   0 <= (          0) <  +inf      
%    Number of linear variables
%      When the Hessian is approximated, it is assumed that the first
%      num_linear_variables variables are linear.  The Hessian is then not
%      approximated in this space.  If the get_number_of_nonlinear_variables
%      method in the TNLP is implemented, this option is ignored.
% 
% kappa_d                                0 <= (      1e-05) <  +inf      
%    Weight for linear damping term (to handle one-sided bounds).
%      (see Section 3.7 in implementation paper.)
% 
% bound_relax_factor                     0 <= (      1e-08) <  +inf      
%    Factor for initial relaxation of the bounds.
%      Before start of the optimization, the bounds given by the user are
%      relaxed.  This option sets the factor for this relaxation.  If it is set
%      to zero, then then bounds relaxation is disabled. (See Eqn.(35) in
%      implementation paper.)
% 
% honor_original_bounds         ("yes")
%    Indicates whether final points should be projected into original bounds.
%      Ipopt might relax the bounds during the optimization (see, e.g., option
%      "bound_relax_factor").  This option determines whether the final point
%      should be projected back into the user-provide original bounds after the
%      optimization.
%    Possible values:
%     - no                      [Leave final point unchanged]
%     - yes                     [Project final point back into original bounds]
% 
% check_derivatives_for_naninf  ("no")
%    Indicates whether it is desired to check for Nan/Inf in derivative matrices
%      Activating this option will cause an error if an invalid number is
%      detected in the constraint Jacobians or the Lagrangian Hessian.  If this
%      is not activated, the test is skipped, and the algorithm might proceed
%      with invalid numbers and fail.
%    Possible values:
%     - no                      [Don't check (faster).]
%     - yes                     [Check Jacobians and Hessian for Nan and Inf.]
% 
% jac_c_constant                ("no")
%    Indicates whether all equality constraints are linear
%      Activating this option will cause Ipopt to ask for the Jacobian of the
%      equality constraints only once from the NLP and reuse this information
%      later.
%    Possible values:
%     - no                      [Don't assume that all equality constraints are
%                                linear]
%     - yes                     [Assume that equality constraints Jacobian are
%                                constant]
% 
% jac_d_constant                ("no")
%    Indicates whether all inequality constraints are linear
%      Activating this option will cause Ipopt to ask for the Jacobian of the
%      inequality constraints only once from the NLP and reuse this information
%      later.
%    Possible values:
%     - no                      [Don't assume that all inequality constraints
%                                are linear]
%     - yes                     [Assume that equality constraints Jacobian are
%                                constant]
% 
% hessian_constant              ("no")
%    Indicates whether the problem is a quadratic problem
%      Activating this option will cause Ipopt to ask for the Hessian of the
%      Lagrangian function only once from the NLP and reuse this information
%      later.
%    Possible values:
%     - no                      [Assume that Hessian changes]
%     - yes                     [Assume that Hessian is constant]
% 
% 
% 
% ### Initialization ###
% 
% bound_push                             0 <  (       0.01) <  +inf      
%    Desired minimum absolute distance from the initial point to bound.
%      Determines how much the initial point might have to be modified in order
%      to be sufficiently inside the bounds (together with "bound_frac").  (This
%      is kappa_1 in Section 3.6 of implementation paper.)
% 
% bound_frac                             0 <  (       0.01) <= 0.5       
%    Desired minimum relative distance from the initial point to bound.
%      Determines how much the initial point might have to be modified in order
%      to be sufficiently inside the bounds (together with "bound_push").  (This
%      is kappa_2 in Section 3.6 of implementation paper.)
% 
% slack_bound_push                       0 <  (       0.01) <  +inf      
%    Desired minimum absolute distance from the initial slack to bound.
%      Determines how much the initial slack variables might have to be modified
%      in order to be sufficiently inside the inequality bounds (together with
%      "slack_bound_frac").  (This is kappa_1 in Section 3.6 of implementation
%      paper.)
% 
% slack_bound_frac                       0 <  (       0.01) <= 0.5       
%    Desired minimum relative distance from the initial slack to bound.
%      Determines how much the initial slack variables might have to be modified
%      in order to be sufficiently inside the inequality bounds (together with
%      "slack_bound_push").  (This is kappa_2 in Section 3.6 of implementation
%      paper.)
% 
% constr_mult_init_max                   0 <= (       1000) <  +inf      
%    Maximum allowed least-square guess of constraint multipliers.
%      Determines how large the initial least-square guesses of the constraint
%      multipliers are allowed to be (in max-norm). If the guess is larger than
%      this value, it is discarded and all constraint multipliers are set to
%      zero.  This options is also used when initializing the restoration phase.
%      By default, "resto.constr_mult_init_max" (the one used in
%      RestoIterateInitializer) is set to zero.
% 
% bound_mult_init_val                    0 <  (          1) <  +inf      
%    Initial value for the bound multipliers.
%      All dual variables corresponding to bound constraints are initialized to
%      this value.
% 
% bound_mult_init_method        ("constant")
%    Initialization method for bound multipliers
%      This option defines how the iterates for the bound multipliers are
%      initialized.  If "constant" is chosen, then all bound multipliers are
%      initialized to the value of "bound_mult_init_val".  If "mu-based" is
%      chosen, the each value is initialized to the the value of "mu_init"
%      divided by the corresponding slack variable.  This latter option might be
%      useful if the starting point is close to the optimal solution.
%    Possible values:
%     - constant                [set all bound multipliers to the value of
%                                bound_mult_init_val]
%     - mu-based                [initialize to mu_init/x_slack]
% 
% least_square_init_primal      ("no")
%    Least square initialization of the primal variables
%      If set to yes, Ipopt ignores the user provided point and solves a least
%      square problem for the primal variables (x and s), to fit the linearized
%      equality and inequality constraints.  This might be useful if the user
%      doesn't know anything about the starting point, or for solving an LP or
%      QP.
%    Possible values:
%     - no                      [take user-provided point]
%     - yes                     [overwrite user-provided point with least-square
%                                estimates]
% 
% least_square_init_duals       ("no")
%    Least square initialization of all dual variables
%      If set to yes, Ipopt tries to compute least-square multipliers
%      (considering ALL dual variables).  If successful, the bound multipliers
%      are possibly corrected to be at least bound_mult_init_val. This might be
%      useful if the user doesn't know anything about the starting point, or for
%      solving an LP or QP.  This overwrites option "bound_mult_init_method".
%    Possible values:
%     - no                      [use bound_mult_init_val and least-square
%                                equality constraint multipliers]
%     - yes                     [overwrite user-provided point with least-square
%                                estimates]
% 
% 
% 
% ### Barrier Parameter Update ###
% 
% mu_max_fact                            0 <  (       1000) <  +inf      
%    Factor for initialization of maximum value for barrier parameter.
%      This option determines the upper bound on the barrier parameter.  This
%      upper bound is computed as the average complementarity at the initial
%      point times the value of this option. (Only used if option "mu_strategy"
%      is chosen as "adaptive".)
% 
% mu_max                                 0 <  (     100000) <  +inf      
%    Maximum value for barrier parameter.
%      This option specifies an upper bound on the barrier parameter in the
%      adaptive mu selection mode.  If this option is set, it overwrites the
%      effect of mu_max_fact. (Only used if option "mu_strategy" is chosen as
%      "adaptive".)
% 
% mu_min                                 0 <  (      1e-11) <  +inf      
%    Minimum value for barrier parameter.
%      This option specifies the lower bound on the barrier parameter in the
%      adaptive mu selection mode. By default, it is set to the minimum of 1e-11
%      and min("tol","compl_inf_tol")/("barrier_tol_factor"+1), which should be
%      a reasonable value. (Only used if option "mu_strategy" is chosen as
%      "adaptive".)
% 
% adaptive_mu_globalization     ("obj-constr-filter")
%    Globalization strategy for the adaptive mu selection mode.
%      To achieve global convergence of the adaptive version, the algorithm has
%      to switch to the monotone mode (Fiacco-McCormick approach) when
%      convergence does not seem to appear.  This option sets the criterion used
%      to decide when to do this switch. (Only used if option "mu_strategy" is
%      chosen as "adaptive".)
%    Possible values:
%     - kkt-error               [nonmonotone decrease of kkt-error]
%     - obj-constr-filter       [2-dim filter for objective and constraint
%                                violation]
%     - never-monotone-mode     [disables globalization]
% 
% adaptive_mu_kkterror_red_iters         0 <= (          4) <  +inf      
%    Maximum number of iterations requiring sufficient progress.
%      For the "kkt-error" based globalization strategy, sufficient progress
%      must be made for "adaptive_mu_kkterror_red_iters" iterations. If this
%      number of iterations is exceeded, the globalization strategy switches to
%      the monotone mode.
% 
% adaptive_mu_kkterror_red_fact          0 <  (     0.9999) <  1         
%    Sufficient decrease factor for "kkt-error" globalization strategy.
%      For the "kkt-error" based globalization strategy, the error must decrease
%      by this factor to be deemed sufficient decrease.
% 
% filter_margin_fact                     0 <  (      1e-05) <  1         
%    Factor determining width of margin for obj-constr-filter adaptive
%    globalization strategy.
%      When using the adaptive globalization strategy, "obj-constr-filter",
%      sufficient progress for a filter entry is defined as follows: (new obj) <
%      (filter obj) - filter_margin_fact*(new constr-viol) OR (new constr-viol)
%      < (filter constr-viol) - filter_margin_fact*(new constr-viol).  For the
%      description of the "kkt-error-filter" option see "filter_max_margin".
% 
% filter_max_margin                      0 <  (          1) <  +inf      
%    Maximum width of margin in obj-constr-filter adaptive globalization
%    strategy.
% 
% adaptive_mu_restore_previous_iterate("no")
%    Indicates if the previous iterate should be restored if the monotone mode
%    is entered.
%      When the globalization strategy for the adaptive barrier algorithm
%      switches to the monotone mode, it can either start from the most recent
%      iterate (no), or from the last iterate that was accepted (yes).
%    Possible values:
%     - no                      [don't restore accepted iterate]
%     - yes                     [restore accepted iterate]
% 
% adaptive_mu_monotone_init_factor         0 <  (        0.8) <  +inf      
%    Determines the initial value of the barrier parameter when switching to the
%    monotone mode.
%      When the globalization strategy for the adaptive barrier algorithm
%      switches to the monotone mode and fixed_mu_oracle is chosen as
%      "average_compl", the barrier parameter is set to the current average
%      complementarity times the value of "adaptive_mu_monotone_init_factor".
% 
% adaptive_mu_kkt_norm_type     ("2-norm-squared")
%    Norm used for the KKT error in the adaptive mu globalization strategies.
%      When computing the KKT error for the globalization strategies, the norm
%      to be used is specified with this option. Note, this options is also used
%      in the QualityFunctionMuOracle.
%    Possible values:
%     - 1-norm                  [use the 1-norm (abs sum)]
%     - 2-norm-squared          [use the 2-norm squared (sum of squares)]
%     - max-norm                [use the infinity norm (max)]
%     - 2-norm                  [use 2-norm]
% 
% mu_strategy                   ("monotone")
%    Update strategy for barrier parameter.
%      Determines which barrier parameter update strategy is to be used.
%    Possible values:
%     - monotone                [use the monotone (Fiacco-McCormick) strategy]
%     - adaptive                [use the adaptive update strategy]
% 
% mu_oracle                     ("quality-function")
%    Oracle for a new barrier parameter in the adaptive strategy.
%      Determines how a new barrier parameter is computed in each "free-mode"
%      iteration of the adaptive barrier parameter strategy. (Only considered if
%      "adaptive" is selected for option "mu_strategy").
%    Possible values:
%     - probing                 [Mehrotra's probing heuristic]
%     - loqo                    [LOQO's centrality rule]
%     - quality-function        [minimize a quality function]
% 
% fixed_mu_oracle               ("average_compl")
%    Oracle for the barrier parameter when switching to fixed mode.
%      Determines how the first value of the barrier parameter should be
%      computed when switching to the "monotone mode" in the adaptive strategy.
%      (Only considered if "adaptive" is selected for option "mu_strategy".)
%    Possible values:
%     - probing                 [Mehrotra's probing heuristic]
%     - loqo                    [LOQO's centrality rule]
%     - quality-function        [minimize a quality function]
%     - average_compl           [base on current average complementarity]
% 
% mu_init                                0 <  (        0.1) <  +inf      
%    Initial value for the barrier parameter.
%      This option determines the initial value for the barrier parameter (mu). 
%      It is only relevant in the monotone, Fiacco-McCormick version of the
%      algorithm. (i.e., if "mu_strategy" is chosen as "monotone")
% 
% barrier_tol_factor                     0 <  (         10) <  +inf      
%    Factor for mu in barrier stop test.
%      The convergence tolerance for each barrier problem in the monotone mode
%      is the value of the barrier parameter times "barrier_tol_factor". This
%      option is also used in the adaptive mu strategy during the monotone mode.
%      (This is kappa_epsilon in implementation paper).
% 
% mu_linear_decrease_factor              0 <  (        0.2) <  1         
%    Determines linear decrease rate of barrier parameter.
%      For the Fiacco-McCormick update procedure the new barrier parameter mu is
%      obtained by taking the minimum of mu*"mu_linear_decrease_factor" and
%      mu^"superlinear_decrease_power".  (This is kappa_mu in implementation
%      paper.) This option is also used in the adaptive mu strategy during the
%      monotone mode.
% 
% mu_superlinear_decrease_power          1 <  (        1.5) <  2         
%    Determines superlinear decrease rate of barrier parameter.
%      For the Fiacco-McCormick update procedure the new barrier parameter mu is
%      obtained by taking the minimum of mu*"mu_linear_decrease_factor" and
%      mu^"superlinear_decrease_power".  (This is theta_mu in implementation
%      paper.) This option is also used in the adaptive mu strategy during the
%      monotone mode.
% 
% mu_allow_fast_monotone_decrease("yes")
%    Allow skipping of barrier problem if barrier test is already met.
%      If set to "no", the algorithm enforces at least one iteration per barrier
%      problem, even if the barrier test is already met for the updated barrier
%      parameter.
%    Possible values:
%     - no                      [Take at least one iteration per barrier problem]
%     - yes                     [Allow fast decrease of mu if barrier test it met]
% 
% tau_min                                0 <  (       0.99) <  1         
%    Lower bound on fraction-to-the-boundary parameter tau.
%      (This is tau_min in the implementation paper.)  This option is also used
%      in the adaptive mu strategy during the monotone mode.
% 
% sigma_max                              0 <  (        100) <  +inf      
%    Maximum value of the centering parameter.
%      This is the upper bound for the centering parameter chosen by the quality
%      function based barrier parameter update. (Only used if option "mu_oracle"
%      is set to "quality-function".)
% 
% sigma_min                              0 <= (      1e-06) <  +inf      
%    Minimum value of the centering parameter.
%      This is the lower bound for the centering parameter chosen by the quality
%      function based barrier parameter update. (Only used if option "mu_oracle"
%      is set to "quality-function".)
% 
% quality_function_norm_type    ("2-norm-squared")
%    Norm used for components of the quality function.
%      (Only used if option "mu_oracle" is set to "quality-function".)
%    Possible values:
%     - 1-norm                  [use the 1-norm (abs sum)]
%     - 2-norm-squared          [use the 2-norm squared (sum of squares)]
%     - max-norm                [use the infinity norm (max)]
%     - 2-norm                  [use 2-norm]
% 
% quality_function_centrality   ("none")
%    The penalty term for centrality that is included in quality function.
%      This determines whether a term is added to the quality function to
%      penalize deviation from centrality with respect to complementarity.  The
%      complementarity measure here is the xi in the Loqo update rule. (Only
%      used if option "mu_oracle" is set to "quality-function".)
%    Possible values:
%     - none                    [no penalty term is added]
%     - log                     [complementarity * the log of the centrality
%                                measure]
%     - reciprocal              [complementarity * the reciprocal of the
%                                centrality measure]
%     - cubed-reciprocal        [complementarity * the reciprocal of the
%                                centrality measure cubed]
% 
% quality_function_balancing_term("none")
%    The balancing term included in the quality function for centrality.
%      This determines whether a term is added to the quality function that
%      penalizes situations where the complementarity is much smaller than dual
%      and primal infeasibilities. (Only used if option "mu_oracle" is set to
%      "quality-function".)
%    Possible values:
%     - none                    [no balancing term is added]
%     - cubic                   [Max(0,Max(dual_inf,primal_inf)-compl)^3]
% 
% quality_function_max_section_steps         0 <= (          8) <  +inf      
%    Maximum number of search steps during direct search procedure determining
%    the optimal centering parameter.
%      The golden section search is performed for the quality function based mu
%      oracle. (Only used if option "mu_oracle" is set to "quality-function".)
% 
% quality_function_section_sigma_tol         0 <= (       0.01) <  1         
%    Tolerance for the section search procedure determining the optimal
%    centering parameter (in sigma space).
%      The golden section search is performed for the quality function based mu
%      oracle. (Only used if option "mu_oracle" is set to "quality-function".)
% 
% quality_function_section_qf_tol         0 <= (          0) <  1         
%    Tolerance for the golden section search procedure determining the optimal
%    centering parameter (in the function value space).
%      The golden section search is performed for the quality function based mu
%      oracle. (Only used if option "mu_oracle" is set to "quality-function".)
% 
% 
% 
% ### Line Search ###
% 
% alpha_red_factor                       0 <  (        0.5) <  1         
%    Fractional reduction of the trial step size in the backtracking line search.
%      At every step of the backtracking line search, the trial step size is
%      reduced by this factor.
% 
% accept_every_trial_step       ("no")
%    Always accept the first trial step.
%      Setting this option to "yes" essentially disables the line search and
%      makes the algorithm take aggressive steps, without global convergence
%      guarantees.
%    Possible values:
%     - no                      [don't arbitrarily accept the full step]
%     - yes                     [always accept the full step]
% 
% accept_after_max_steps                -1 <= (         -1) <  +inf      
%    Accept a trial point after maximal this number of steps.
%      Even if it does not satisfy line search conditions.
% 
% alpha_for_y                   ("primal")
%    Method to determine the step size for constraint multipliers.
%      This option determines how the step size (alpha_y) will be calculated
%      when updating the constraint multipliers.
%    Possible values:
%     - primal                  [use primal step size]
%     - bound-mult              [use step size for the bound multipliers (good
%                                for LPs)]
%     - min                     [use the min of primal and bound multipliers]
%     - max                     [use the max of primal and bound multipliers]
%     - full                    [take a full step of size one]
%     - min-dual-infeas         [choose step size minimizing new dual
%                                infeasibility]
%     - safer-min-dual-infeas   [like "min_dual_infeas", but safeguarded by
%                                "min" and "max"]
%     - primal-and-full         [use the primal step size, and full step if
%                                delta_x <= alpha_for_y_tol]
%     - dual-and-full           [use the dual step size, and full step if
%                                delta_x <= alpha_for_y_tol]
%     - acceptor                [Call LSAcceptor to get step size for y]
% 
% alpha_for_y_tol                        0 <= (         10) <  +inf      
%    Tolerance for switching to full equality multiplier steps.
%      This is only relevant if "alpha_for_y" is chosen "primal-and-full" or
%      "dual-and-full".  The step size for the equality constraint multipliers
%      is taken to be one if the max-norm of the primal step is less than this
%      tolerance.
% 
% tiny_step_tol                          0 <= (2.22045e-15) <  +inf      
%    Tolerance for detecting numerically insignificant steps.
%      If the search direction in the primal variables (x and s) is, in relative
%      terms for each component, less than this value, the algorithm accepts the
%      full step without line search.  If this happens repeatedly, the algorithm
%      will terminate with a corresponding exit message. The default value is 10
%      times machine precision.
% 
% tiny_step_y_tol                        0 <= (       0.01) <  +inf      
%    Tolerance for quitting because of numerically insignificant steps.
%      If the search direction in the primal variables (x and s) is, in relative
%      terms for each component, repeatedly less than tiny_step_tol, and the
%      step in the y variables is smaller than this threshold, the algorithm
%      will terminate.
% 
% watchdog_shortened_iter_trigger         0 <= (         10) <  +inf      
%    Number of shortened iterations that trigger the watchdog.
%      If the number of successive iterations in which the backtracking line
%      search did not accept the first trial point exceeds this number, the
%      watchdog procedure is activated.  Choosing "0" here disables the watchdog
%      procedure.
% 
% watchdog_trial_iter_max                1 <= (          3) <  +inf      
%    Maximum number of watchdog iterations.
%      This option determines the number of trial iterations allowed before the
%      watchdog procedure is aborted and the algorithm returns to the stored
%      point.
% 
% theta_max_fact                         0 <  (      10000) <  +inf      
%    Determines upper bound for constraint violation in the filter.
%      The algorithmic parameter theta_max is determined as theta_max_fact times
%      the maximum of 1 and the constraint violation at initial point.  Any
%      point with a constraint violation larger than theta_max is unacceptable
%      to the filter (see Eqn. (21) in the implementation paper).
% 
% theta_min_fact                         0 <  (     0.0001) <  +inf      
%    Determines constraint violation threshold in the switching rule.
%      The algorithmic parameter theta_min is determined as theta_min_fact times
%      the maximum of 1 and the constraint violation at initial point.  The
%      switching rules treats an iteration as an h-type iteration whenever the
%      current constraint violation is larger than theta_min (see paragraph
%      before Eqn. (19) in the implementation paper).
% 
% eta_phi                                0 <  (      1e-08) <  0.5       
%    Relaxation factor in the Armijo condition.
%      (See Eqn. (20) in the implementation paper)
% 
% delta                                  0 <  (          1) <  +inf      
%    Multiplier for constraint violation in the switching rule.
%      (See Eqn. (19) in the implementation paper.)
% 
% s_phi                                  1 <  (        2.3) <  +inf      
%    Exponent for linear barrier function model in the switching rule.
%      (See Eqn. (19) in the implementation paper.)
% 
% s_theta                                1 <  (        1.1) <  +inf      
%    Exponent for current constraint violation in the switching rule.
%      (See Eqn. (19) in the implementation paper.)
% 
% gamma_phi                              0 <  (      1e-08) <  1         
%    Relaxation factor in the filter margin for the barrier function.
%      (See Eqn. (18a) in the implementation paper.)
% 
% gamma_theta                            0 <  (      1e-05) <  1         
%    Relaxation factor in the filter margin for the constraint violation.
%      (See Eqn. (18b) in the implementation paper.)
% 
% alpha_min_frac                         0 <  (       0.05) <  1         
%    Safety factor for the minimal step size (before switching to restoration
%    phase).
%      (This is gamma_alpha in Eqn. (20) in the implementation paper.)
% 
% max_soc                                0 <= (          4) <  +inf      
%    Maximum number of second order correction trial steps at each iteration.
%      Choosing 0 disables the second order corrections. (This is p^{max} of
%      Step A-5.9 of Algorithm A in the implementation paper.)
% 
% kappa_soc                              0 <  (       0.99) <  +inf      
%    Factor in the sufficient reduction rule for second order correction.
%      This option determines how much a second order correction step must
%      reduce the constraint violation so that further correction steps are
%      attempted.  (See Step A-5.9 of Algorithm A in the implementation paper.)
% 
% obj_max_inc                            1 <  (          5) <  +inf      
%    Determines the upper bound on the acceptable increase of barrier objective
%    function.
%      Trial points are rejected if they lead to an increase in the barrier
%      objective function by more than obj_max_inc orders of magnitude.
% 
% max_filter_resets                      0 <= (          5) <  +inf      
%    Maximal allowed number of filter resets
%      A positive number enables a heuristic that resets the filter, whenever in
%      more than "filter_reset_trigger" successive iterations the last rejected
%      trial steps size was rejected because of the filter.  This option
%      determine the maximal number of resets that are allowed to take place.
% 
% filter_reset_trigger                   1 <= (          5) <  +inf      
%    Number of iterations that trigger the filter reset.
%      If the filter reset heuristic is active and the number of successive
%      iterations in which the last rejected trial step size was rejected
%      because of the filter, the filter is reset.
% 
% corrector_type                ("none")
%    The type of corrector steps that should be taken (unsupported!).
%      If "mu_strategy" is "adaptive", this option determines what kind of
%      corrector steps should be tried.
%    Possible values:
%     - none                    [no corrector]
%     - affine                  [corrector step towards mu=0]
%     - primal-dual             [corrector step towards current mu]
% 
% skip_corr_if_neg_curv         ("yes")
%    Skip the corrector step in negative curvature iteration (unsupported!).
%      The corrector step is not tried if negative curvature has been
%      encountered during the computation of the search direction in the current
%      iteration. This option is only used if "mu_strategy" is "adaptive".
%    Possible values:
%     - no                      [don't skip]
%     - yes                     [skip]
% 
% skip_corr_in_monotone_mode    ("yes")
%    Skip the corrector step during monotone barrier parameter mode
%    (unsupported!).
%      The corrector step is not tried if the algorithm is currently in the
%      monotone mode (see also option "barrier_strategy").This option is only
%      used if "mu_strategy" is "adaptive".
%    Possible values:
%     - no                      [don't skip]
%     - yes                     [skip]
% 
% corrector_compl_avrg_red_fact          0 <  (          1) <  +inf      
%    Complementarity tolerance factor for accepting corrector step
%    (unsupported!).
%      This option determines the factor by which complementarity is allowed to
%      increase for a corrector step to be accepted.
% 
% nu_init                                0 <  (      1e-06) <  +inf      
%    Initial value of the penalty parameter.
% 
% nu_inc                                 0 <  (     0.0001) <  +inf      
%    Increment of the penalty parameter.
% 
% rho                                    0 <  (        0.1) <  1         
%    Value in penalty parameter update formula.
% 
% kappa_sigma                            0 <  (      1e+10) <  +inf      
%    Factor limiting the deviation of dual variables from primal estimates.
%      If the dual variables deviate from their primal estimates, a correction
%      is performed. (See Eqn. (16) in the implementation paper.) Setting the
%      value to less than 1 disables the correction.
% 
% recalc_y                      ("no")
%    Tells the algorithm to recalculate the equality and inequality multipliers
%    as least square estimates.
%      This asks the algorithm to recompute the multipliers, whenever the
%      current infeasibility is less than recalc_y_feas_tol. Choosing yes might
%      be helpful in the quasi-Newton option.  However, each recalculation
%      requires an extra factorization of the linear system.  If a limited
%      memory quasi-Newton option is chosen, this is used by default.
%    Possible values:
%     - no                      [use the Newton step to update the multipliers]
%     - yes                     [use least-square multiplier estimates]
% 
% recalc_y_feas_tol                      0 <  (      1e-06) <  +inf      
%    Feasibility threshold for recomputation of multipliers.
%      If recalc_y is chosen and the current infeasibility is less than this
%      value, then the multipliers are recomputed.
% 
% slack_move                             0 <= (1.81899e-12) <  +inf      
%    Correction size for very small slacks.
%      Due to numerical issues or the lack of an interior, the slack variables
%      might become very small.  If a slack becomes very small compared to
%      machine precision, the corresponding bound is moved slightly.  This
%      parameter determines how large the move should be.  Its default value is
%      mach_eps^{3/4}.  (See also end of Section 3.5 in implementation paper -
%      but actual implementation might be somewhat different.)
% 
% 
% 
% ### Warm Start ###
% 
% warm_start_init_point         ("no")
%    Warm-start for initial point
%      Indicates whether this optimization should use a warm start
%      initialization, where values of primal and dual variables are given
%      (e.g., from a previous optimization of a related problem.)
%    Possible values:
%     - no                      [do not use the warm start initialization]
%     - yes                     [use the warm start initialization]
% 
% warm_start_same_structure     ("no")
%    Indicates whether a problem with a structure identical to the previous one
%    is to be solved.
%      If "yes" is chosen, then the algorithm assumes that an NLP is now to be
%      solved, whose structure is identical to one that already was considered
%      (with the same NLP object).
%    Possible values:
%     - no                      [Assume this is a new problem.]
%     - yes                     [Assume this is problem has known structure]
% 
% warm_start_bound_push                  0 <  (      0.001) <  +inf      
%    same as bound_push for the regular initializer.
% 
% warm_start_bound_frac                  0 <  (      0.001) <= 0.5       
%    same as bound_frac for the regular initializer.
% 
% warm_start_slack_bound_push            0 <  (      0.001) <  +inf      
%    same as slack_bound_push for the regular initializer.
% 
% warm_start_slack_bound_frac            0 <  (      0.001) <= 0.5       
%    same as slack_bound_frac for the regular initializer.
% 
% warm_start_mult_bound_push             0 <  (      0.001) <  +inf      
%    same as mult_bound_push for the regular initializer.
% 
% warm_start_mult_init_max            -inf <  (      1e+06) <  +inf      
%    Maximum initial value for the equality multipliers.
% 
% warm_start_entire_iterate     ("no")
%    Tells algorithm whether to use the GetWarmStartIterate method in the NLP.
%    Possible values:
%     - no                      [call GetStartingPoint in the NLP]
%     - yes                     [call GetWarmStartIterate in the NLP]
% 
% 
% 
% ### Linear Solver ###
% 
% linear_solver                 ("mumps")
%    Linear solver used for step computations.
%      Determines which linear algebra package is to be used for the solution of
%      the augmented linear system (for obtaining the search directions). Note,
%      the code must have been compiled with the linear solver you want to
%      choose. Depending on your Ipopt installation, not all options are
%      available.
%    Possible values:
%     - ma27                    [use the Harwell routine MA27]
%     - ma57                    [use the Harwell routine MA57]
%     - pardiso                 [use the Pardiso package]
%     - wsmp                    [use WSMP package]
%     - mumps                   [use MUMPS package]
%     - custom                  [use custom linear solver]
% 
% linear_system_scaling         ("none")
%    Method for scaling the linear system.
%      Determines the method used to compute symmetric scaling factors for the
%      augmented system (see also the "linear_scaling_on_demand" option).  This
%      scaling is independent of the NLP problem scaling.  By default, MC19 is
%      only used if MA27 or MA57 are selected as linear solvers. This option is
%      only available if Ipopt has been compiled with MC19.
%    Possible values:
%     - none                    [no scaling will be performed]
%     - mc19                    [use the Harwell routine MC19]
% 
% linear_scaling_on_demand      ("yes")
%    Flag indicating that linear scaling is only done if it seems required.
%      This option is only important if a linear scaling method (e.g., mc19) is
%      used.  If you choose "no", then the scaling factors are computed for
%      every linear system from the start.  This can be quite expensive.
%      Choosing "yes" means that the algorithm will start the scaling method
%      only when the solutions to the linear system seem not good, and then use
%      it until the end.
%    Possible values:
%     - no                      [Always scale the linear system.]
%     - yes                     [Start using linear system scaling if solutions
%                                seem not good.]
% 
% 
% 
% ### Step Calculation ###
% 
% mehrotra_algorithm            ("no")
%    Indicates if we want to do Mehrotra's algorithm.
%      If set to yes, Ipopt runs as Mehrotra's predictor-corrector algorithm.
%      This works usually very well for LPs and convex QPs.  This automatically
%      disables the line search, and chooses the (unglobalized) adaptive mu
%      strategy with the "probing" oracle, and uses "corrector_type=affine"
%      without any safeguards; you should not set any of those options
%      explicitly in addition.  Also, unless otherwise specified, the values of
%      "bound_push", "bound_frac", and "bound_mult_init_val" are set more
%      aggressive, and sets "alpha_for_y=bound_mult".
%    Possible values:
%     - no                      [Do the usual Ipopt algorithm.]
%     - yes                     [Do Mehrotra's predictor-corrector algorithm.]
% 
% fast_step_computation         ("no")
%    Indicates if the linear system should be solved quickly.
%      If set to yes, the algorithm assumes that the linear system that is
%      solved to obtain the search direction, is solved sufficiently well. In
%      that case, no residuals are computed, and the computation of the search
%      direction is a little faster.
%    Possible values:
%     - no                      [Verify solution of linear system by computing
%                                residuals.]
%     - yes                     [Trust that linear systems are solved well.]
% 
% min_refinement_steps                   0 <= (          1) <  +inf      
%    Minimum number of iterative refinement steps per linear system solve.
%      Iterative refinement (on the full unsymmetric system) is performed for
%      each right hand side.  This option determines the minimum number of
%      iterative refinements (i.e. at least "min_refinement_steps" iterative
%      refinement steps are enforced per right hand side.)
% 
% max_refinement_steps                   0 <= (         10) <  +inf      
%    Maximum number of iterative refinement steps per linear system solve.
%      Iterative refinement (on the full unsymmetric system) is performed for
%      each right hand side.  This option determines the maximum number of
%      iterative refinement steps.
% 
% residual_ratio_max                     0 <  (      1e-10) <  +inf      
%    Iterative refinement tolerance
%      Iterative refinement is performed until the residual test ratio is less
%      than this tolerance (or until "max_refinement_steps" refinement steps are
%      performed).
% 
% residual_ratio_singular                0 <  (      1e-05) <  +inf      
%    Threshold for declaring linear system singular after failed iterative
%    refinement.
%      If the residual test ratio is larger than this value after failed
%      iterative refinement, the algorithm pretends that the linear system is
%      singular.
% 
% residual_improvement_factor            0 <  (          1) <  +inf      
%    Minimal required reduction of residual test ratio in iterative refinement.
%      If the improvement of the residual test ratio made by one iterative
%      refinement step is not better than this factor, iterative refinement is
%      aborted.
% 
% neg_curv_test_tol                      0 <  (          0) <  +inf      
%    Tolerance for heuristic to ignore wrong inertia.
%      If positive, incorrect inertia in the augmented system is ignored, and we
%      test if the direction is a direction of positive curvature.  This
%      tolerance determines when the direction is considered to be sufficiently
%      positive.
% 
% max_hessian_perturbation               0 <  (      1e+20) <  +inf      
%    Maximum value of regularization parameter for handling negative curvature.
%      In order to guarantee that the search directions are indeed proper
%      descent directions, Ipopt requires that the inertia of the (augmented)
%      linear system for the step computation has the correct number of negative
%      and positive eigenvalues. The idea is that this guides the algorithm away
%      from maximizers and makes Ipopt more likely converge to first order
%      optimal points that are minimizers. If the inertia is not correct, a
%      multiple of the identity matrix is added to the Hessian of the Lagrangian
%      in the augmented system. This parameter gives the maximum value of the
%      regularization parameter. If a regularization of that size is not enough,
%      the algorithm skips this iteration and goes to the restoration phase.
%      (This is delta_w^max in the implementation paper.)
% 
% min_hessian_perturbation               0 <= (      1e-20) <  +inf      
%    Smallest perturbation of the Hessian block.
%      The size of the perturbation of the Hessian block is never selected
%      smaller than this value, unless no perturbation is necessary. (This is
%      delta_w^min in implementation paper.)
% 
% perturb_inc_fact_first                 1 <  (        100) <  +inf      
%    Increase factor for x-s perturbation for very first perturbation.
%      The factor by which the perturbation is increased when a trial value was
%      not sufficient - this value is used for the computation of the very first
%      perturbation and allows a different value for for the first perturbation
%      than that used for the remaining perturbations. (This is bar_kappa_w^+ in
%      the implementation paper.)
% 
% perturb_inc_fact                       1 <  (          8) <  +inf      
%    Increase factor for x-s perturbation.
%      The factor by which the perturbation is increased when a trial value was
%      not sufficient - this value is used for the computation of all
%      perturbations except for the first. (This is kappa_w^+ in the
%      implementation paper.)
% 
% perturb_dec_fact                       0 <  (   0.333333) <  1         
%    Decrease factor for x-s perturbation.
%      The factor by which the perturbation is decreased when a trial value is
%      deduced from the size of the most recent successful perturbation. (This
%      is kappa_w^- in the implementation paper.)
% 
% first_hessian_perturbation             0 <  (     0.0001) <  +inf      
%    Size of first x-s perturbation tried.
%      The first value tried for the x-s perturbation in the inertia correction
%      scheme.(This is delta_0 in the implementation paper.)
% 
% jacobian_regularization_value          0 <= (      1e-08) <  +inf      
%    Size of the regularization for rank-deficient constraint Jacobians.
%      (This is bar delta_c in the implementation paper.)
% 
% jacobian_regularization_exponent         0 <= (       0.25) <  +inf      
%    Exponent for mu in the regularization for rank-deficient constraint
%    Jacobians.
%      (This is kappa_c in the implementation paper.)
% 
% perturb_always_cd             ("no")
%    Active permanent perturbation of constraint linearization.
%      This options makes the delta_c and delta_d perturbation be used for the
%      computation of every search direction.  Usually, it is only used when the
%      iteration matrix is singular.
%    Possible values:
%     - no                      [perturbation only used when required]
%     - yes                     [always use perturbation]
% 
% 
% 
% ### Restoration Phase ###
% 
% expect_infeasible_problem     ("no")
%    Enable heuristics to quickly detect an infeasible problem.
%      This options is meant to activate heuristics that may speed up the
%      infeasibility determination if you expect that there is a good chance for
%      the problem to be infeasible.  In the filter line search procedure, the
%      restoration phase is called more quickly than usually, and more reduction
%      in the constraint violation is enforced before the restoration phase is
%      left. If the problem is square, this option is enabled automatically.
%    Possible values:
%     - no                      [the problem probably be feasible]
%     - yes                     [the problem has a good chance to be infeasible]
% 
% expect_infeasible_problem_ctol         0 <= (      0.001) <  +inf      
%    Threshold for disabling "expect_infeasible_problem" option.
%      If the constraint violation becomes smaller than this threshold, the
%      "expect_infeasible_problem" heuristics in the filter line search are
%      disabled. If the problem is square, this options is set to 0.
% 
% expect_infeasible_problem_ytol         0 <  (      1e+08) <  +inf      
%    Multiplier threshold for activating "expect_infeasible_problem" option.
%      If the max norm of the constraint multipliers becomes larger than this
%      value and "expect_infeasible_problem" is chosen, then the restoration
%      phase is entered.
% 
% start_with_resto              ("no")
%    Tells algorithm to switch to restoration phase in first iteration.
%      Setting this option to "yes" forces the algorithm to switch to the
%      feasibility restoration phase in the first iteration. If the initial
%      point is feasible, the algorithm will abort with a failure.
%    Possible values:
%     - no                      [don't force start in restoration phase]
%     - yes                     [force start in restoration phase]
% 
% soft_resto_pderror_reduction_factor         0 <= (     0.9999) <  +inf      
%    Required reduction in primal-dual error in the soft restoration phase.
%      The soft restoration phase attempts to reduce the primal-dual error with
%      regular steps. If the damped primal-dual step (damped only to satisfy the
%      fraction-to-the-boundary rule) is not decreasing the primal-dual error by
%      at least this factor, then the regular restoration phase is called.
%      Choosing "0" here disables the soft restoration phase.
% 
% max_soft_resto_iters                   0 <= (         10) <  +inf      
%    Maximum number of iterations performed successively in soft restoration
%    phase.
%      If the soft restoration phase is performed for more than so many
%      iterations in a row, the regular restoration phase is called.
% 
% required_infeasibility_reduction         0 <= (        0.9) <  1         
%    Required reduction of infeasibility before leaving restoration phase.
%      The restoration phase algorithm is performed, until a point is found that
%      is acceptable to the filter and the infeasibility has been reduced by at
%      least the fraction given by this option.
% 
% max_resto_iter                         0 <= (    3000000) <  +inf      
%    Maximum number of successive iterations in restoration phase.
%      The algorithm terminates with an error message if the number of
%      iterations successively taken in the restoration phase exceeds this
%      number.
% 
% evaluate_orig_obj_at_resto_trial("yes")
%    Determines if the original objective function should be evaluated at
%    restoration phase trial points.
%      Setting this option to "yes" makes the restoration phase algorithm
%      evaluate the objective function of the original problem at every trial
%      point encountered during the restoration phase, even if this value is not
%      required.  In this way, it is guaranteed that the original objective
%      function can be evaluated without error at all accepted iterates;
%      otherwise the algorithm might fail at a point where the restoration phase
%      accepts an iterate that is good for the restoration phase problem, but
%      not the original problem.  On the other hand, if the evaluation of the
%      original objective is expensive, this might be costly.
%    Possible values:
%     - no                      [skip evaluation]
%     - yes                     [evaluate at every trial point]
% 
% resto_penalty_parameter                0 <  (       1000) <  +inf      
%    Penalty parameter in the restoration phase objective function.
%      This is the parameter rho in equation (31a) in the Ipopt implementation
%      paper.
% 
% bound_mult_reset_threshold             0 <= (       1000) <  +inf      
%    Threshold for resetting bound multipliers after the restoration phase.
%      After returning from the restoration phase, the bound multipliers are
%      updated with a Newton step for complementarity.  Here, the change in the
%      primal variables during the entire restoration phase is taken to be the
%      corresponding primal Newton step. However, if after the update the
%      largest bound multiplier exceeds the threshold specified by this option,
%      the multipliers are all reset to 1.
% 
% constr_mult_reset_threshold            0 <= (          0) <  +inf      
%    Threshold for resetting equality and inequality multipliers after
%    restoration phase.
%      After returning from the restoration phase, the constraint multipliers
%      are recomputed by a least square estimate.  This option triggers when
%      those least-square estimates should be ignored.
% 
% 
% 
% ### Derivative Checker ###
% 
% derivative_test               ("none")
%    Enable derivative checker
%      If this option is enabled, a (slow!) derivative test will be performed
%      before the optimization.  The test is performed at the user provided
%      starting point and marks derivative values that seem suspicious
%    Possible values:
%     - none                    [do not perform derivative test]
%     - first-order             [perform test of first derivatives at starting
%                                point]
%     - second-order            [perform test of first and second derivatives at
%                                starting point]
%     - only-second-order       [perform test of second derivatives at starting
%                                point]
% 
% derivative_test_first_index           -2 <= (         -2) <  +inf      
%    Index of first quantity to be checked by derivative checker
%      If this is set to -2, then all derivatives are checked.  Otherwise, for
%      the first derivative test it specifies the first variable for which the
%      test is done (counting starts at 0).  For second derivatives, it
%      specifies the first constraint for which the test is done; counting of
%      constraint indices starts at 0, and -1 refers to the objective function
%      Hessian.
% 
% derivative_test_perturbation           0 <  (      1e-08) <  +inf      
%    Size of the finite difference perturbation in derivative test.
%      This determines the relative perturbation of the variable entries.
% 
% derivative_test_tol                    0 <  (     0.0001) <  +inf      
%    Threshold for indicating wrong derivative.
%      If the relative deviation of the estimated derivative from the given one
%      is larger than this value, the corresponding derivative is marked as
%      wrong.
% 
% derivative_test_print_all     ("no")
%    Indicates whether information for all estimated derivatives should be
%    printed.
%      Determines verbosity of derivative checker.
%    Possible values:
%     - no                      [Print only suspect derivatives]
%     - yes                     [Print all derivatives]
% 
% jacobian_approximation        ("exact")
%    Specifies technique to compute constraint Jacobian
%    Possible values:
%     - exact                   [user-provided derivatives]
%     - finite-difference-values [user-provided structure, values by finite
%                                differences]
% 
% findiff_perturbation                   0 <  (      1e-07) <  +inf      
%    Size of the finite difference perturbation for derivative approximation.
%      This determines the relative perturbation of the variable entries.
% 
% point_perturbation_radius              0 <= (         10) <  +inf      
%    Maximal perturbation of an evaluation point.
%      If a random perturbation of a points is required, this number indicates
%      the maximal perturbation.  This is for example used when determining the
%      center point at which the finite difference derivative test is executed.
% 
% 
% 
% ### Hessian Approximation ###
% 
% limited_memory_max_history             0 <= (          6) <  +inf      
%    Maximum size of the history for the limited quasi-Newton Hessian
%    approximation.
%      This option determines the number of most recent iterations that are
%      taken into account for the limited-memory quasi-Newton approximation.
% 
% limited_memory_update_type    ("bfgs")
%    Quasi-Newton update formula for the limited memory approximation.
%      Determines which update formula is to be used for the limited-memory
%      quasi-Newton approximation.
%    Possible values:
%     - bfgs                    [BFGS update (with skipping)]
%     - sr1                     [SR1 (not working well)]
% 
% limited_memory_initialization ("scalar1")
%    Initialization strategy for the limited memory quasi-Newton approximation.
%      Determines how the diagonal Matrix B_0 as the first term in the limited
%      memory approximation should be computed.
%    Possible values:
%     - scalar1                 [sigma = s^Ty/s^Ts]
%     - scalar2                 [sigma = y^Ty/s^Ty]
%     - constant                [sigma = limited_memory_init_val]
% 
% limited_memory_init_val                0 <  (          1) <  +inf      
%    Value for B0 in low-rank update.
%      The starting matrix in the low rank update, B0, is chosen to be this
%      multiple of the identity in the first iteration (when no updates have
%      been performed yet), and is constantly chosen as this value, if
%      "limited_memory_initialization" is "constant".
% 
% limited_memory_init_val_max            0 <  (      1e+08) <  +inf      
%    Upper bound on value for B0 in low-rank update.
%      The starting matrix in the low rank update, B0, is chosen to be this
%      multiple of the identity in the first iteration (when no updates have
%      been performed yet), and is constantly chosen as this value, if
%      "limited_memory_initialization" is "constant".
% 
% limited_memory_init_val_min            0 <  (      1e-08) <  +inf      
%    Lower bound on value for B0 in low-rank update.
%      The starting matrix in the low rank update, B0, is chosen to be this
%      multiple of the identity in the first iteration (when no updates have
%      been performed yet), and is constantly chosen as this value, if
%      "limited_memory_initialization" is "constant".
% 
% limited_memory_max_skipping            1 <= (          2) <  +inf      
%    Threshold for successive iterations where update is skipped.
%      If the update is skipped more than this number of successive iterations,
%      we quasi-Newton approximation is reset.
% 
% hessian_approximation         ("exact")
%    Indicates what Hessian information is to be used.
%      This determines which kind of information for the Hessian of the
%      Lagrangian function is used by the algorithm.
%    Possible values:
%     - exact                   [Use second derivatives provided by the NLP.]
%     - limited-memory          [Perform a limited-memory quasi-Newton
%                                approximation]
% 
% hessian_approximation_space   ("nonlinear-variables")
%    Indicates in which subspace the Hessian information is to be approximated.
%    Possible values:
%     - nonlinear-variables     [only in space of nonlinear variables.]
%     - all-variables           [in space of all variables (without slacks)]
% 
% 
% 
% ### MA27 Linear Solver ###
% 
% ma27_pivtol                            0 <  (      1e-08) <  1         
%    Pivot tolerance for the linear solver MA27.
%      A smaller number pivots for sparsity, a larger number pivots for
%      stability.  This option is only available if Ipopt has been compiled with
%      MA27.
% 
% ma27_pivtolmax                         0 <  (     0.0001) <  1         
%    Maximum pivot tolerance for the linear solver MA27.
%      Ipopt may increase pivtol as high as pivtolmax to get a more accurate
%      solution to the linear system.  This option is only available if Ipopt
%      has been compiled with MA27.
% 
% ma27_liw_init_factor                   1 <= (          5) <  +inf      
%    Integer workspace memory for MA27.
%      The initial integer workspace memory = liw_init_factor * memory required
%      by unfactored system. Ipopt will increase the workspace size by
%      meminc_factor if required.  This option is only available if Ipopt has
%      been compiled with MA27.
% 
% ma27_la_init_factor                    1 <= (          5) <  +inf      
%    Real workspace memory for MA27.
%      The initial real workspace memory = la_init_factor * memory required by
%      unfactored system. Ipopt will increase the workspace size by
%      meminc_factor if required.  This option is only available if  Ipopt has
%      been compiled with MA27.
% 
% ma27_meminc_factor                     1 <= (         10) <  +inf      
%    Increment factor for workspace size for MA27.
%      If the integer or real workspace is not large enough, Ipopt will increase
%      its size by this factor.  This option is only available if Ipopt has been
%      compiled with MA27.
% 
% ma27_skip_inertia_check       ("no")
%    Always pretend inertia is correct.
%      Setting this option to "yes" essentially disables inertia check. This
%      option makes the algorithm non-robust and easily fail, but it might give
%      some insight into the necessity of inertia control.
%    Possible values:
%     - no                      [check inertia]
%     - yes                     [skip inertia check]
% 
% ma27_ignore_singularity       ("no")
%    Enables MA27's ability to solve a linear system even if the matrix is
%    singular.
%      Setting this option to "yes" means that Ipopt will call MA27 to compute
%      solutions for right hand sides, even if MA27 has detected that the matrix
%      is singular (but is still able to solve the linear system). In some cases
%      this might be better than using Ipopt's heuristic of small perturbation
%      of the lower diagonal of the KKT matrix.
%    Possible values:
%     - no                      [Don't have MA27 solve singular systems]
%     - yes                     [Have MA27 solve singular systems]
% 
% 
% 
% ### MA57 Linear Solver ###
% 
% ma57_pivtol                            0 <  (      1e-08) <  1         
%    Pivot tolerance for the linear solver MA57.
%      A smaller number pivots for sparsity, a larger number pivots for
%      stability. This option is only available if Ipopt has been compiled with
%      MA57.
% 
% ma57_pivtolmax                         0 <  (     0.0001) <  1         
%    Maximum pivot tolerance for the linear solver MA57.
%      Ipopt may increase pivtol as high as ma57_pivtolmax to get a more
%      accurate solution to the linear system.  This option is only available if
%      Ipopt has been compiled with MA57.
% 
% ma57_pre_alloc                         1 <= (          3) <  +inf      
%    Safety factor for work space memory allocation for the linear solver MA57.
%      If 1 is chosen, the suggested amount of work space is used.  However,
%      choosing a larger number might avoid reallocation if the suggest values
%      do not suffice.  This option is only available if Ipopt has been compiled
%      with MA57.
% 
% ma57_pivot_order                       0 <= (          5) <= 5         
%    Controls pivot order in MA57
%      This is INCTL(6) in MA57.
% 
% 
% 
% ### Pardiso Linear Solver ###
% 
% pardiso_matching_strategy     ("complete+2x2")
%    Matching strategy to be used by Pardiso
%      This is IPAR(13) in Pardiso manual.  This option is only available if
%      Ipopt has been compiled with Pardiso.
%    Possible values:
%     - complete                [Match complete (IPAR(13)=1)]
%     - complete+2x2            [Match complete+2x2 (IPAR(13)=2)]
%     - constraints             [Match constraints (IPAR(13)=3)]
% 
% pardiso_redo_symbolic_fact_only_if_inertia_wrong("no")
%    Toggle for handling case when elements were perturbed by Pardiso.
%      This option is only available if Ipopt has been compiled with Pardiso.
%    Possible values:
%     - no                      [Always redo symbolic factorization when
%                                elements were perturbed]
%     - yes                     [Only redo symbolic factorization when elements
%                                were perturbed if also the inertia was wrong]
% 
% pardiso_repeated_perturbation_means_singular("no")
%    Interpretation of perturbed elements.
%      This option is only available if Ipopt has been compiled with Pardiso.
%    Possible values:
%     - no                      [Don't assume that matrix is singular if
%                                elements were perturbed after recent symbolic
%                                factorization]
%     - yes                     [Assume that matrix is singular if elements were
%                                perturbed after recent symbolic factorization]
% 
% pardiso_out_of_core_power              0 <= (          0) <  +inf      
%    Enables out-of-core variant of Pardiso
%      Setting this option to a positive integer k makes Pardiso work in the
%      out-of-core variant where the factor is split in 2^k subdomains.  This is
%      IPARM(50) in the Pardiso manual.  This option is only available if Ipopt
%      has been compiled with Pardiso.
% 
% pardiso_msglvl                         0 <= (          0) <  +inf      
%    Pardiso message level
%      This determines the amount of analysis output from the Pardiso solver.
%      This is MSGLVL in the Pardiso manual.
% 
% pardiso_skip_inertia_check    ("no")
%    Always pretent inertia is correct.
%      Setting this option to "yes" essentially disables inertia check. This
%      option makes the algorithm non-robust and easily fail, but it might give
%      some insight into the necessity of inertia control.
%    Possible values:
%     - no                      [check inertia]
%     - yes                     [skip inertia check]
% 
% pardiso_max_iter                       1 <= (        500) <  +inf      
%    Maximum number of Krylov-Subspace Iteration
%      DPARM(1)
% 
% pardiso_iter_relative_tol              0 <  (      1e-06) <  1         
%    Relative Residual Convergence
%      DPARM(2)
% 
% pardiso_iter_coarse_size               1 <= (       5000) <  +inf      
%    Maximum Size of Coarse Grid Matrix
%      DPARM(3)
% 
% pardiso_iter_max_levels                1 <= (      10000) <  +inf      
%    Maximum Size of Grid Levels
%      DPARM(4)
% 
% pardiso_iter_dropping_factor           0 <  (        0.5) <  1         
%    dropping value for incomplete factor
%      DPARM(5)
% 
% pardiso_iter_dropping_schur            0 <  (        0.1) <  1         
%    dropping value for sparsify schur complement factor
%      DPARM(6)
% 
% pardiso_iter_max_row_fill              1 <= (   10000000) <  +inf      
%    max fill for each row
%      DPARM(7)
% 
% pardiso_iter_inverse_norm_factor         1 <  (      5e+06) <  +inf      
%    
%      DPARM(8)
% 
% pardiso_iterative             ("no")
%    Switch on iterative solver in Pardiso library
%    Possible values:
%     - no                      []
%     - yes                     []
% 
% pardiso_max_droptol_corrections         1 <= (          4) <  +inf      
%    Maximal number of decreases of drop tolerance during one solve.
%      This is relevant only for iterative Pardiso options.
% 
% 
% 
% ### Mumps Linear Solver ###
% 
% mumps_pivtol                           0 <= (      1e-06) <= 1         
%    Pivot tolerance for the linear solver MUMPS.
%      A smaller number pivots for sparsity, a larger number pivots for
%      stability.  This option is only available if Ipopt has been compiled with
%      MUMPS.
% 
% mumps_pivtolmax                        0 <= (        0.1) <= 1         
%    Maximum pivot tolerance for the linear solver MUMPS.
%      Ipopt may increase pivtol as high as pivtolmax to get a more accurate
%      solution to the linear system.  This option is only available if Ipopt
%      has been compiled with MUMPS.
% 
% mumps_mem_percent                      0 <= (       1000) <  +inf      
%    Percentage increase in the estimated working space for MUMPS.
%      In MUMPS when significant extra fill-in is caused by numerical pivoting,
%      larger values of mumps_mem_percent may help use the workspace more
%      efficiently.  On the other hand, if memory requirement are too large at
%      the very beginning of the optimization, choosing a much smaller value for
%      this option, such as 5, might reduce memory requirements.
% 
% mumps_permuting_scaling                0 <= (          7) <= 7         
%    Controls permuting and scaling in MUMPS
%      This is ICNTL(6) in MUMPS.
% 
% mumps_pivot_order                      0 <= (          7) <= 7         
%    Controls pivot order in MUMPS
%      This is ICNTL(7) in MUMPS.
% 
% mumps_scaling                         -2 <= (         77) <= 77        
%    Controls scaling in MUMPS
%      This is ICNTL(8) in MUMPS.
% 
% mumps_dep_tol                       -inf <  (         -1) <  +inf      
%    Pivot threshold for detection of linearly dependent constraints in MUMPS.
%      When MUMPS is used to determine linearly dependent constraints, this is
%      determines the threshold for a pivot to be considered zero.  This is
%      CNTL(3) in MUMPS.
% 
% 
% 
% ### MA28 Linear Solver ###
% 
% ma28_pivtol                            0 <  (       0.01) <= 1         
%    Pivot tolerance for linear solver MA28.
%      This is used when MA28 tries to find the dependent constraints.
% 
% 
% 
% ### Uncategorized ###
% 
% warm_start_target_mu                -inf <  (          0) <  +inf      
%    Unsupported!