MOI.OPTIMAL status but infeasible solution #212
Description
g = [1, 2, 3]
model = Model(Mosek.Optimizer)
@variables(model, begin
p[eachindex(g)] >= 0
Ω[eachindex(g)]
end)
@constraint(model, sum(p) == 1)
@constraint(model, [i=eachindex(g)], [1, p[i], Ω[i]] in MOI.ExponentialCone())
@objective(model, Max, sum(p .* g) + 0.0 * sum(Ω))
latex_formulation(model)
In this model (that was wrong it should've been [Ω[i], p[i], 1] in MOI.ExponentialCone()) but regardless, when optimizing the model reaches optimality but the constraint sum(p) == 1 is not satisfied.
optimize!(model)Problem
Name :
Objective sense : max
Type : CONIC (conic optimization problem)
Constraints : 10
Cones : 3
Scalar variables : 15
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : max
Type : CONIC (conic optimization problem)
Constraints : 10
Cones : 3
Scalar variables : 15
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 18
Optimizer - solved problem : the primal
Optimizer - Constraints : 1
Optimizer - Cones : 3
Optimizer - Scalar variables : 9 conic : 9
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 1 after factor : 1
Factor - dense dim. : 0 flops : 1.30e+01
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.8e+00 3.8e+00 6.3e+00 0.00e+00 4.830612010e+00 -2.483515197e+00 1.0e+00 0.00
1 2.1e-01 4.4e-01 7.8e-01 -3.14e-01 3.018859342e+00 1.785519550e-01 1.2e-01 0.00
2 3.2e-02 6.6e-02 9.7e-02 1.22e-01 2.222927263e+00 9.727063870e-01 1.7e-02 0.00
3 6.4e-03 1.3e-02 4.2e-03 9.07e-01 2.117075200e+00 1.993968819e+00 3.5e-03 0.00
4 1.0e-03 2.2e-03 4.9e-04 6.46e-01 2.270224493e+00 2.231262552e+00 5.7e-04 0.00
5 2.2e-04 4.7e-04 1.1e-04 1.72e-01 2.412201194e+00 2.383051296e+00 1.2e-04 0.00
6 4.7e-05 9.7e-05 1.8e-05 3.65e-01 2.475835861e+00 2.459845099e+00 2.5e-05 0.00
7 1.7e-05 3.4e-05 7.4e-06 5.85e-02 2.541615728e+00 2.522650249e+00 9.0e-06 0.00
8 3.4e-06 7.1e-06 1.1e-06 4.22e-01 2.574995923e+00 2.566225740e+00 1.9e-06 0.00
9 1.3e-06 2.7e-06 4.7e-07 9.78e-02 2.619258121e+00 2.607690011e+00 7.1e-07 0.00
10 2.9e-07 6.0e-07 7.2e-08 4.67e-01 2.637973135e+00 2.632572432e+00 1.6e-07 0.00
11 1.1e-07 2.4e-07 3.5e-08 9.35e-02 2.671000491e+00 2.663023181e+00 6.2e-08 0.00
12 2.4e-08 5.1e-08 5.0e-09 4.87e-01 2.684172907e+00 2.680637816e+00 1.3e-08 0.00
13 8.1e-09 1.7e-08 2.1e-09 6.02e-02 2.713815830e+00 2.707895975e+00 4.4e-09 0.00
14 1.9e-09 3.9e-09 3.2e-10 5.33e-01 2.721289042e+00 2.718900850e+00 1.0e-09 0.00
15 6.4e-10 1.3e-09 1.4e-10 4.71e-02 2.743921987e+00 2.739772216e+00 3.5e-10 0.00
16 1.4e-10 2.9e-10 2.0e-11 4.96e-01 2.751292501e+00 2.749514064e+00 7.5e-11 0.00
17 3.9e-11 8.2e-11 7.8e-12 2.26e-02 2.771969917e+00 2.768655197e+00 2.2e-11 0.00
18 1.0e-11 2.1e-11 1.2e-12 5.96e-01 2.775657313e+00 2.774381591e+00 5.5e-12 0.00
19 3.5e-12 7.2e-12 5.8e-13 3.15e-02 2.789987283e+00 2.787650836e+00 1.9e-12 0.00
20 7.8e-13 1.6e-12 8.9e-14 4.81e-01 2.795357759e+00 2.794265755e+00 4.2e-13 0.00
21 2.4e-13 5.0e-13 3.4e-14 2.99e-02 2.805805254e+00 2.804135451e+00 1.3e-13 0.00
22 4.8e-14 1.0e-13 5.7e-15 2.71e-01 2.813539824e+00 2.812365436e+00 2.6e-14 0.00
23 1.5e-14 3.1e-14 2.2e-15 -2.40e-03 2.822450247e+00 2.820697208e+00 8.3e-15 0.00
24 3.5e-15 7.4e-15 3.8e-16 3.85e-01 2.827082078e+00 2.826125811e+00 1.9e-15 0.00
25 9.5e-16 2.0e-15 1.3e-16 -4.85e-02 2.836327732e+00 2.834682575e+00 5.2e-16 0.00
26 2.2e-16 4.6e-16 2.4e-17 3.36e-01 2.840379465e+00 2.839404879e+00 1.2e-16 0.00
27 7.3e-17 1.5e-16 9.7e-18 -3.25e-02 2.846980326e+00 2.845491145e+00 4.0e-17 0.00
28 1.8e-17 3.6e-17 1.7e-18 3.83e-01 2.850175560e+00 2.849408256e+00 9.6e-18 0.00
29 5.5e-18 1.1e-17 6.6e-19 -3.01e-02 2.856158109e+00 2.854939799e+00 3.0e-18 0.00
30 1.1e-18 2.4e-18 1.1e-19 2.61e-01 2.860147432e+00 2.859335447e+00 6.2e-19 0.00
31 4.0e-19 8.4e-19 4.8e-20 9.84e-03 2.864801063e+00 2.863626950e+00 2.2e-19 0.00
32 1.0e-19 2.1e-19 8.5e-21 4.07e-01 2.867208551e+00 2.866604890e+00 5.5e-20 0.00
33 3.1e-20 6.3e-20 3.4e-21 -5.87e-02 2.872464596e+00 2.871410124e+00 1.7e-20 0.00
34 7.1e-21 1.5e-20 5.9e-22 3.37e-01 2.874830484e+00 2.874233898e+00 3.8e-21 0.00
35 2.4e-21 4.9e-21 2.5e-22 -3.94e-02 2.878902315e+00 2.877980792e+00 1.3e-21 0.00
36 6.1e-22 1.2e-21 4.4e-23 3.81e-01 2.880864248e+00 2.880386453e+00 3.2e-22 0.00
37 2.3e-22 3.8e-22 1.8e-23 -3.92e-02 2.884610205e+00 2.883845993e+00 1.0e-22 0.00
38 4.8e-23 7.9e-23 3.0e-24 2.45e-01 2.887246096e+00 2.886726479e+00 2.1e-23 0.00
39 9.3e-23 2.8e-23 1.3e-24 6.01e-03 2.890275629e+00 2.889520967e+00 7.3e-24 0.00
40 4.1e-23 7.0e-24 2.3e-25 4.04e-01 2.891854464e+00 2.891463497e+00 1.8e-24 0.00
41 1.7e-23 2.0e-24 9.0e-26 -7.17e-02 2.895496116e+00 2.894787867e+00 5.3e-25 0.00
42 6.4e-24 4.7e-25 1.5e-26 3.56e-01 2.896958288e+00 2.896575882e+00 1.3e-25 0.00
43 1.1e-23 1.6e-25 6.6e-27 -4.71e-02 2.899796396e+00 2.899186023e+00 4.2e-26 0.00
44 2.6e-24 4.2e-26 1.1e-27 3.80e-01 2.901144025e+00 2.900826139e+00 1.0e-26 0.00
45 1.2e-24 1.5e-26 4.8e-28 -3.93e-02 2.903739795e+00 2.903228499e+00 3.2e-27 0.00
46 3.0e-25 8.5e-28 4.5e-29 2.39e-01 2.905594920e+00 2.905240326e+00 6.6e-28 0.00
47 8.9e-26 4.0e-28 6.0e-30 -3.37e-03 2.907754518e+00 2.907232163e+00 2.3e-28 0.00
Optimizer terminated. Time: 0.00
the solution found is
[2.3028378190668097e-14, 2.402867139391792e-14, 7.127137945447063e-13]which violates the sum(p) == 1 constraint.
Is this a bug? The correct problem works fine BTW.
i'm using mosek 9.3.18, mosek.jl 1.2.1 adn, mosek tools 0.12.0 on julia 1.6