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Implement QCQP duals #321

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Oct 5, 2020
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Implement QCQP duals #321

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8f9cd83
Implement QCQP duals
odow Oct 1, 2020
1d1dda1
Explain parameter choice
odow Oct 4, 2020
fb46992
Simplify dual calculations
odow Oct 4, 2020
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90 changes: 81 additions & 9 deletions src/MOI/MOI_wrapper.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2787,15 +2787,63 @@ function MOI.get(
return _dual_multiplier(model) * p[]
end

# function MOI.get(
# model::Optimizer, attr::MOI.ConstraintDual,
# c::MOI.ConstraintIndex{MOI.ScalarQuadraticFunction{Float64}, <:Any}
# )
# _throw_if_optimize_in_progress(model, attr)
# MOI.check_result_index_bounds(model, attr)
# pi = model.cached_solution.quadratic_dual[_info(model, c).row]
# return _dual_multiplier(model) * pi
# end
function MOI.get(
model::Optimizer,
attr::MOI.ConstraintDual,
c::MOI.ConstraintIndex{MOI.ScalarQuadraticFunction{Float64}, <:Any},
)
# For more information on QCP duals, see
# https://www.ibm.com/support/knowledgecenter/SSSA5P_12.10.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/cont_optim/qcp/17_QCP_duals.html
_throw_if_optimize_in_progress(model, attr)
MOI.check_result_index_bounds(model, attr)
# The derivative of a quadratic f(x) = x^TQx + a^Tx + b <= 0 is
# ∇f(x) = Q^Tx + Qx + a
# The dual is undefined if x is at the point of the cone. This can only be
# checked to numeric tolerances. We use `cone_top_tol`.
cone_top, cone_top_tol = true, 1e-6
x = zeros(length(model.variable_info))
ret = CPXgetx(model.env, model.lp, x, 0, length(x) - 1)
_check_ret(model, ret)
∇f = zeros(length(x))
a_i, a_v, qrow, qcol, qval = _CPXgetqconstr(model, c)
for (i, j, v) in zip(qrow, qcol, qval)
∇f[i + 1] += v * x[j + 1]
∇f[j + 1] += v * x[i + 1]
if abs(x[i + 1]) > cone_top_tol || abs(x[j + 1]) > cone_top_tol
cone_top = false
end
end
for (i, v) in zip(a_i, a_v)
∇f[i + 1] += v
if abs(x[i + 1]) > cone_top_tol
cone_top = false
end
end
# TODO(odow): if at top of cone (x = 0) dual multiplier is ill-formed.
if cone_top
return NaN
end
qind = Cint(_info(model, c).row - 1)
nz_p, surplus_p = Ref{Cint}(), Ref{Cint}()
CPXgetqconstrdslack(
model.env, model.lp, qind, nz_p, C_NULL, C_NULL, 0, surplus_p
)
ind = Vector{Cint}(undef, -surplus_p[])
val = Vector{Cdouble}(undef, -surplus_p[])
ret = CPXgetqconstrdslack(
model.env, model.lp, qind, nz_p, ind, val, -surplus_p[], surplus_p
)
_check_ret(model, ret)
∇f_max, ∇f_i = findmax(abs.(∇f))
if ∇f_max > cone_top_tol
for (i, v) in zip(ind, val)
if i + 1 == ∇f_i
return _dual_multiplier(model) * v / ∇f[∇f_i]
end
end
end
return 0.0
end

function MOI.get(model::Optimizer, attr::MOI.ObjectiveValue)
_throw_if_optimize_in_progress(model, attr)
Expand Down Expand Up @@ -3464,3 +3512,27 @@ function MOI.set(
return
end

function MOI.get(
model::Optimizer,
::MOI.ConstraintDual,
c::MOI.ConstraintIndex{MOI.VectorOfVariables, MOI.SecondOrderCone},
)
f = MOI.get(model, MOI.ConstraintFunction(), c)
qind = Cint(_info(model, c).row - 1)
surplus_p = Ref{Cint}()
CPXgetqconstrdslack(
model.env, model.lp, qind, C_NULL, C_NULL, C_NULL, 0, surplus_p
)
ind = Vector{Cint}(undef, -surplus_p[])
val = Vector{Cdouble}(undef, -surplus_p[])
ret = CPXgetqconstrdslack(
model.env, model.lp, qind, C_NULL, ind, val, -surplus_p[], surplus_p
)
_check_ret(model, ret)
slack = zeros(length(model.variable_info))
for (i, v) in zip(ind, val)
slack[i + 1] += v
end
z = _dual_multiplier(model)
return [z * slack[_info(model, v).column] for v in f.variables]
end
58 changes: 21 additions & 37 deletions test/MathOptInterface/MOI_wrapper.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -12,14 +12,11 @@ const CONFIG = MOIT.TestConfig()

const OPTIMIZER = CPLEX.Optimizer()
MOI.set(OPTIMIZER, MOI.Silent(), true)
const BRIDGED_OPTIMIZER = MOI.Bridges.full_bridge_optimizer(OPTIMIZER, Float64)
# Turn off presolve reductions so CPLEX will generate infeasibility
# certificates.
MOI.set(OPTIMIZER, MOI.RawParameter("CPX_PARAM_REDUCE"), 0)
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const CERTIFICATE_OPTIMIZER = CPLEX.Optimizer()
MOI.set(CERTIFICATE_OPTIMIZER, MOI.Silent(), true)
MOI.set(CERTIFICATE_OPTIMIZER, MOI.RawParameter("CPX_PARAM_REDUCE"), 0)
MOI.set(CERTIFICATE_OPTIMIZER, MOI.RawParameter("CPX_PARAM_PRELINEAR"), 0)
const BRIDGED_CERTIFICATE_OPTIMIZER =
MOI.Bridges.full_bridge_optimizer(CERTIFICATE_OPTIMIZER, Float64)
const BRIDGED_OPTIMIZER = MOI.Bridges.full_bridge_optimizer(OPTIMIZER, Float64)

function test_basic_constraint_tests()
MOIT.basic_constraint_tests(BRIDGED_OPTIMIZER, CONFIG; exclude = [
Expand Down Expand Up @@ -62,12 +59,7 @@ function test_unittest()
# TODO(odow): bug! We can't delete a vector of variables if one is in
# a second order cone.
"delete_soc_variables",

# CPLEX returns INFEASIBLE_OR_UNBOUNDED without extra parameters.
# See below for the test.
"solve_unbounded_model",
])
MOIT.solve_unbounded_model(CERTIFICATE_OPTIMIZER, CONFIG)
end

function test_modificationtest()
Expand All @@ -76,18 +68,11 @@ end

function test_contlineartest()
MOIT.contlineartest(BRIDGED_OPTIMIZER, CONFIG, [
# These tests require extra parameters to be set.
"linear8a", "linear8b", "linear8c",

# TODO(odow): This test requests the infeasibility certificate of a
# variable bound.
"linear12"
])

MOIT.linear8atest(CERTIFICATE_OPTIMIZER, CONFIG)
MOIT.linear8btest(CERTIFICATE_OPTIMIZER, CONFIG)
MOIT.linear8ctest(CERTIFICATE_OPTIMIZER, CONFIG)

MOIT.linear12test(OPTIMIZER, MOIT.TestConfig(infeas_certificates=false))
end

Expand All @@ -101,35 +86,34 @@ end

function test_contquadratictest()
MOIT.contquadratictest(
BRIDGED_CERTIFICATE_OPTIMIZER,
# TODO(odow): duals for quadratic problems.
MOIT.TestConfig(duals = false, atol = 1e-3, rtol = 1e-3),
BRIDGED_OPTIMIZER,
MOIT.TestConfig(atol = 1e-3, rtol = 1e-3),
["ncqcp"], # CPLEX doesn't support non-convex problems
)
end

function test_contconic()
MOIT.lintest(BRIDGED_OPTIMIZER, CONFIG, [
# These tests require extra parameters to be set.
"lin3", "lin4"
])

MOIT.lin3test(BRIDGED_CERTIFICATE_OPTIMIZER, CONFIG)
MOIT.lin4test(BRIDGED_CERTIFICATE_OPTIMIZER, CONFIG)

# TODO(odow): duals for SOC constraints.
soc_config = MOIT.TestConfig(duals = false, atol=5e-3)
MOIT.lintest(BRIDGED_OPTIMIZER, CONFIG)

MOIT.soctest(BRIDGED_OPTIMIZER, soc_config, [
"soc3"
])
soc_config = MOIT.TestConfig(atol=5e-3)

# TODO(odow): investigate why infeasibility certificates not generated for
# SOC.
MOIT.soctest(BRIDGED_OPTIMIZER, soc_config, ["soc3"])
MOIT.soc3test(
BRIDGED_OPTIMIZER,
MOIT.TestConfig(duals = false, infeas_certificates = false, atol = 1e-3)
MOIT.TestConfig(atol = 1e-3, infeas_certificates = false)
)

MOIT.rsoctest(BRIDGED_OPTIMIZER, soc_config)
MOIT.rsoctest(BRIDGED_OPTIMIZER, soc_config, ["rotatedsoc2"])
MOIT.rotatedsoc2test(
BRIDGED_OPTIMIZER,
# Need for `duals = false` fixed by https://github.com/jump-dev/MathOptInterface.jl/pull/1171
# Remove in a future MOI 0.9.18+ release.
MOIT.TestConfig(
atol = 1e-3, infeas_certificates = false, duals = false
),
)

MOIT.geomeantest(BRIDGED_OPTIMIZER, soc_config)
end
Expand Down