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jump_sdp.jl
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jump_sdp.jl
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using JuMP
function test_jump_sdp(solver)
@testset "Semidefinite Programming" begin
@testset "SDP1" begin
# Problem SDP1 - sdo1 from MOSEK docs
# From Mosek.jl/test/mathprogtestextra.jl, under license:
# Copyright (c) 2013 Ulf Worsoe, Mosek ApS
# Permission is hereby granted, free of charge, to any person obtaining a copy of this
# software and associated documentation files (the "Software"), to deal in the Software
# without restriction, including without limitation the rights to use, copy, modify, merge,
# publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons
# to whom the Software is furnished to do so, subject to the following conditions:
# The above copyright notice and this permission notice shall be included in all copies or
# substantial portions of the Software.
#
# | 2 1 0 |
# min | 1 2 1 | . X + x1
# | 0 1 2 |
#
#
# s.t. | 1 0 0 |
# | 0 1 0 | . X + x1 = 1
# | 0 0 1 |
#
# | 1 1 1 |
# | 1 1 1 | . X + x2 + x3 = 1/2
# | 1 1 1 |
#
# (x1,x2,x3) in C^3_q
# X in C_sdp
m = Model(solver=solver)
@variable(m, x[1:3])
@constraint(m, x in MOI.SecondOrderCone(3))
@variable(m, X[1:3, 1:3], PSD)
C = [2 1 0
1 2 1
0 1 2]
A1 = [1 0 0
0 1 0
0 0 1]
A2 = [1 1 1
1 1 1
1 1 1]
@objective(m, Min, vecdot(C, X) + x[1])
@constraint(m, vecdot(A1, X) + x[1] == 1)
@constraint(m, vecdot(A2, X) + x[2] + x[3] == 1/2)
JuMP.solve(m)
@test JuMP.isattached(m)
@test JuMP.hasvariableresult(m)
@test JuMP.terminationstatus(m) == MOI.Success
@test JuMP.primalstatus(m) == MOI.FeasiblePoint
@test JuMP.objectivevalue(m) ≈ 0.705710509 atol=1e-6
xv = JuMP.resultvalue.(x)
Xv = JuMP.resultvalue.(X)
@test vecdot(C, Xv) + xv[1] ≈ 0.705710509 atol=1e-6
@test eigmin(Xv) > -1e-6
end
@testset "Nonsensical SDPs" begin
m = Model()
@test_throws ErrorException @variable(m, unequal[1:5,1:6], PSD)
# Some of these errors happen at compile time, so we can't use @test_throws
@test macroexpand(:(@variable(m, notone[1:5,2:6], PSD))).head == :error
@test macroexpand(:(@variable(m, oneD[1:5], PSD))).head == :error
@test macroexpand(:(@variable(m, threeD[1:5,1:5,1:5], PSD))).head == :error
@test macroexpand(:(@variable(m, psd[2] <= rand(2,2), PSD))).head == :error
@test macroexpand(:(@variable(m, -ones(3,4) <= foo[1:4,1:4] <= ones(4,4), PSD))).head == :error
@test macroexpand(:(@variable(m, -ones(3,4) <= foo[1:4,1:4] <= ones(4,4), Symmetric))).head == :error
@test macroexpand(:(@variable(m, -ones(4,4) <= foo[1:4,1:4] <= ones(4,5), Symmetric))).head == :error
@test macroexpand(:(@variable(m, -rand(5,5) <= nonsymmetric[1:5,1:5] <= rand(5,5), Symmetric))).head == :error
end
# min o max y + X11
# Q11 - 1 = Q22 [y-X12-X21 0 [0 0
# 0 -y] <= 0 0]
# [1 Q11
# Q11 o ] >= 0 -X[2,2] = 1
# Q >= 0 y free
# o free X <= 0
# @testset "Just another SDP" begin
# model = Model(solver=CSDPSolver(printlevel=0))
# @variable(model, Q[1:2, 1:2], PSD)
# c1 = @constraint(model, Q[1,1] - 1 == Q[2,2])
# @variable(model, objective)
# T = [1 Q[1,1]; Q[1,1] objective]
# @test_throws ErrorException SDConstraint(T, 1)
# c2 = JuMP.addconstraint(model, SDConstraint(T, 0))
# @objective(model, Min, objective)
#
# JuMP.solve(m)
#
# @test JuMP.terminationstatus(m) == MOI.Success
# @test JuMP.primalstatus(m) == MOI.FeasiblePoint
#
# @test JuMP.resultvalue(Q) ≈ [1 0; 0 0] atol=1e-3
# @test JuMP.objectivevalue(model) ≈ 1 atol=1e-4
# @test JuMP.resultvalue(objective) ≈ 1 atol=1e-4
# @test getdual(objective) ≈, 0, atol=1e-5
# @test getdual(Q) ≈ [0 0; 0 2] atol=1e-3
# @test getdual(c1) ≈ 2, atol=1e-4 # y
# @test getdual(c2) ≈ [-1 1; 1 -1] atol=1e-3 # X
# end
# The four following tests are from Example 2.11, Example 2.13 and Example 2.27 of:
# Blekherman, G., Parrilo, P. A., & Thomas, R. R. (Eds.).
# Semidefinite optimization and convex algebraic geometry SIAM 2013
# Example 2.11
@testset "SDP variable and optimal objective not rational" begin
# solver = fixscs(solver, 7000000)
m = Model(solver=solver)
@variable(m, X[1:2,1:2], PSD)
c = @constraint(m, X[1,1]+X[2,2] == 1)
@objective(m, Min, 2*X[1,1]+2*X[1,2])
# @test all(isnan.(getdual(X)))
JuMP.solve(m)
@test JuMP.terminationstatus(m) == MOI.Success
@test JuMP.primalstatus(m) == MOI.FeasiblePoint
@test JuMP.objectivevalue(m) ≈ 1-sqrt(2) atol=1e-5
@test JuMP.resultvalue.(X) ≈ [(2-sqrt(2))/4 -1/(2*sqrt(2)); -1/(2*sqrt(2)) (2+sqrt(2))/4] atol=1e-4
# @test getdual(X) ≈ [1+sqrt(2) 1; 1 sqrt(2)-1] atol=1e-4
# @test getdual(c) ≈ 1-sqrt(2) atol=1e-5
end
# # Example 2.13
# @testset "SDP constraint and optimal objective not rational with $solver" for solver in sdp_solvers
# solver = fixscs(solver, 7000000)
# m = Model(solver=solver)
# @variable(m, y)
# c = @SDconstraint(m, [2-y 1; 1 -y] >= 0)
# @objective(m, Max, y)
# @test all(isnan, getdual(c))
# status = solve(m)
#
# @test status == :Optimal
# @test isapprox(getobjectivevalue(m), 1-sqrt(2), atol=1e-5)
# @test isapprox(getvalue(y), 1-sqrt(2), atol=1e-5)
#
# X = getdual(c)
# @test isapprox(getdual(c), [(2-sqrt(2))/4 -1/(2*sqrt(2)); -1/(2*sqrt(2)) (2+sqrt(2))/4], atol=1e-4)
# @test isapprox(getdual(y), 0, atol=1e-5)
# end
#
# # Example 2.27
# # min X[1,1] max y
# # 2X[1,2] = 1 [0 y [1 0
# # X ⪰ 0 y 0] ⪯ 0 0]
# # The dual optimal solution is y=0 and there is a primal solution
# # [ eps 1/2
# # 1/2 1/eps]
# # for any eps > 0 however there is no primal solution with objective value 0.
# @testset "SDP with dual solution not attained with $solver" for solver in sdp_solvers
# solver = fixscs(solver, 7000000)
# m = Model(solver=solver)
# @variable(m, y)
# c = @SDconstraint(m, [0 y; y 0] <= [1 0; 0 0])
# @objective(m, Max, y)
# @test all(isnan, getdual(c))
# status = solve(m)
#
# if contains(string(typeof(solver)),"MosekSolver")
# # Mosek returns Stall on this instance
# # Hack until we fix statuses in MPB
# JuMP.fillConicDuals(m)
# else
# @test status == :Optimal
# end
# @test isapprox(getobjectivevalue(m), 0, atol=1e-5)
# @test isapprox(getvalue(y), 0, atol=1e-5)
#
# X = getdual(c)
# @test isapprox(X[1,1], 0, atol=1e-5)
# @test isapprox(X[1,2], 1/2, atol=1e-5)
# @test isapprox(X[2,1], 1/2, atol=1e-5)
# @test isapprox(getdual(y), 0, atol=1e-5)
# end
@testset "SDP with primal solution not attained" begin
# solver = fixscs(solver, 7000000)
m = Model(solver=solver)
@variable(m, X[1:2,1:2], PSD)
c = @constraint(m, 2*X[1,2] == 1)
@objective(m, Min, X[1,1])
# @test all(isnan, getdual(X))
status = solve(m)
@test JuMP.terminationstatus(m) in [ MOI.Success, MOI.SlowProgress ]
@test JuMP.primalstatus(m) == MOI.FeasiblePoint
@test JuMP.objectivevalue(m) ≈ 0 atol=1e-5
Xval = JuMP.resultvalue.(X)
#Mosek.writedata(m.solverinstance.task,"jump_sdo_1_stalls.task")
#showall(m.solverinstance.task)
#showall(m.solverinstance.task[Sol(Mosek.MSK_SOL_ITR)])
@test Xval[1,1] ≈ 0 atol=1e-5
@test Xval[1,2] ≈ 1/2 atol=1e-5
@test Xval[2,1] ≈ 1/2 atol=1e-5
# @test isapprox(getdual(X), [1 0; 0 0], atol=1e-4)
# @test isapprox(getdual(c), 0, atol=1e-5)
end
@testset "No constraint" begin
m = Model(solver=solver)
@variable(m, X[1:3,1:3], PSD)
@objective(m, Min, trace(X))
JuMP.solve(m)
status = solve(m)
@test JuMP.terminationstatus(m) == MOI.Success
@test JuMP.primalstatus(m) == MOI.FeasiblePoint
@test abs(JuMP.objectivevalue(m)) < 1e-5
@test norm(JuMP.resultvalue.(X)) < 1e-5
#@test isapprox(getdual(X), eye(3), atol=1e-5)
end
end
end