NLExpressions and multiplication / division with numbers

[anriseth]

I guess this is an issue with the complexity of dealing with nonlinear expressions, so this is more of a note for people who might have the same problems:

The Hessian sparsity changes drastically depending on how you set your objectives in nonlinear optimisation. Division is bad, so is multiplication with something like (1 - a) for some scalar a.
The way around these issues is using multiplication with dummy-variables. In the following, let nf2 be a ParametricExpression defined by @defNLExpr:

julia> @setNLObjective(m, :Min, nf2*(1-a))
julia> solve(m)
This is Ipopt version 3.11.9, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:      355
Number of nonzeros in Lagrangian Hessian.............:    61075
*snip*

julia> num = (1-a)
julia> @setNLObjective(m, :Min, nf2*num)
julia> solve(m)
This is Ipopt version 3.11.9, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:      355
Number of nonzeros in Lagrangian Hessian.............:     1495

Likewise, if you want @setNLObjective(m, :Min, nf2 / a). It is better to use b = 1/a and @setNLObjective(m, :Min, nf2 * b)

[mlubin]

Yes, there are a few heuristics in the sparsity detection code. Will be
addressed in the next rewrite.
On Sep 4, 2015 5:22 AM, "Asbjørn Nilsen Riseth" notifications@github.com
wrote:

I guess this is an issue with the complexity of dealing with nonlinear
expressions, so this is more of a note for people who might have the same
problems:

The Hessian sparsity changes drastically depending on how you set your
objectives in nonlinear optimisation. Division is bad, so is multiplication
with something like (1 - a) for some scalar a.
The way around these issues is using multiplication with dummy-variables.
In the following, let nf2 be a ParametricExpression defined by @defNLExpr:

julia> @setNLObjective(m, :Min, nf2*(1-a))
julia> solve(m)
This is Ipopt version 3.11.9, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 355
Number of nonzeros in Lagrangian Hessian.............: 61075_snip_

julia> num = (1-a)
julia> @setNLObjective(m, :Min, nf2*num)
julia> solve(m)
This is Ipopt version 3.11.9, running with linear solver mumps.
NOTE: Other linear solvers might be more efficient (see Ipopt documentation).

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 355
Number of nonzeros in Lagrangian Hessian.............: 1495

Likewise, if you want @setNLObjective(m, :Min, nf2 / a). It is better to
use b = 1/a and @setNLObjective(m, :Min, nf2 * b)

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[mlubin]

I'd recommend using IpoptNLSolver from the AmplNLWriter package as a workaround, but there are some open issues with that.