Hello everybody. I’m using cvx MOSEK solver and everything is ok but the solver ignores one of constraints! there is no warning about using successive approximation method or any complexity due to log,exp and … in objective function. this violation is huge in scale of the problem. here is my code:

```
cvx_begin
cvx_solver MOSEK;
variable x(L*D*N) nonnegative;
variable v(L*D) binary;
variable y(dimm) binary;
minimize(C*x+rho/2*square_pos(norm(AA*x-z-pp+u)));
subject to
-B*x+subplus(B)*b+M*(y-ones(dimm,1))+M*(subplus(H)*v-min(H,0)*v-2)<=zeros(dimm,1);
B*x+subplus(-1*B)*b-M*y+M*(subplus(H)*v-min(H,0)*v-2)<=zeros(dimm,1);
x>=cons;
cvx_end
```

as you can see, the model has three variables named x,y,v. other notations are all parameters. parameters and variables are defined as vectors.

I appreciate you in advance.

Readers can’t reproduce (independently verify) because we don’t have the input data.

Please show us the solver and CVX output, as well as your evidence of “huge” constraint violation.

this huge violation is due to ignored constraints. The output doesn’t show any error or warning.

**output is as below:**

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)

Copyright © MOSEK ApS, Denmark. WWW: mosek.com

Platform: Windows/64-X86

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 31

Cones : 2

Scalar variables : 59

Matrix variables : 0

Integer variables : 8

Optimizer started.

Mixed integer optimizer started.

Threads used: 2

Presolve started.

Presolve terminated. Time = 0.00

Presolved problem: 17 variables, 10 constraints, 24 non-zeros

Presolved problem: 0 general integer, 4 binary, 13 continuous

Clique table size: 0

BRANCHES RELAXS ACT_NDS DEPTH BEST_INT_OBJ BEST_RELAX_OBJ REL_GAP(%) TIME

0 1 1 0 NA 3.3366666759e+02 NA 0.0

0 1 1 0 3.3366667593e+02 3.3366666759e+02 2.50e-06 0.0

An optimal solution satisfying the relative gap tolerance of 1.00e-02(%) has been located.

The relative gap is 2.50e-06(%).

Objective of best integer solution : 3.336666759278e+02

Best objective bound : 3.336666675906e+02

Construct solution objective : Not employed

User objective cut value : Not employed

Number of cuts generated : 0

Number of branches : 0

Number of relaxations solved : 1

Number of interior point iterations: 14

Number of simplex iterations : 0

Time spend presolving the root : 0.00

Time spend optimizing the root : 0.05

Mixed integer optimizer terminated. Time: 0.05

Optimizer terminated. Time: 0.06

Integer solution solution summary

Problem status : PRIMAL_FEASIBLE

Solution status : INTEGER_OPTIMAL

Primal. obj: 3.3366667593e+02 nrm: 1e+03 Viol. con: 0e+00 var: 0e+00 cones: 1e-07 itg: 0e+00

Optimizer summary

Optimizer - time: 0.06

Interior-point - iterations : 0 time: 0.00

Basis identification - time: 0.00

Primal - iterations : 0 time: 0.00

Dual - iterations : 0 time: 0.00

Clean primal - iterations : 0 time: 0.00

Clean dual - iterations : 0 time: 0.00

Simplex - time: 0.00

Primal simplex - iterations : 0 time: 0.00

Dual simplex - iterations : 0 time: 0.00

Mixed integer - relaxations: 1 time: 0.05

Status: Solved

Optimal value (cvx_optval): +333.667

Forum readers have no idea what the optimal solution (x, v, y) was, and which constraint(s) were violated.

I’m about to decompose a problem and solve it in parallel. so I’ve provided the input data of one of the subproblem to give it a test if you could. here it is:

L=2;

D=2;

N=4;

rho=4;

M=1000;

dimm=4;

C=[1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0];

AA=[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0];

z=[0

0

0

0];

u=[0

0

0

0];

pp=[76

100

78

80];

B=[-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0

0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0];

b=[74

75

95

83

87

73

75

99

97

76

95

95

76

100

78

80];

cons=[0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0];

H=[-1 0 1 0

-1 0 0 1

0 -1 1 0

0 -1 0 1];

Here is my solution using Mosek, having optimal objective value = 333.5. All constraints are satisfied.

`x`

x =

75.750013252633821

99.750013624545701

77.750012795420091

79.750012829531300

0

0

0

0

0

0

0

0

0

0

0

0

`v`

v =

0

0

0

0

`y`

y =

0

0

0

0

-B*x+subplus(B)**b+M*(y-ones(dimm,1))+M(subplus(H)*v-min(H,0)*v-2)

ans =

1.0e+03 *

-2.906999999542786

-2.920999999576898

-2.882999999170875

-2.896999999204986

`B*x+subplus(-1*B)*b-M*y+M*(subplus(H)*v-min(H,0)*v-2)`

ans =

1.0e+03 *

-1.924000000457214

-1.922000000423103

-1.947000000829126

-1.945000000795014

`x-cons`

ans =

75.750013252633821

99.750013624545701

77.750012795420091

79.750012829531300

0

0

0

0

0

0

0

0

0

0

0

0

It’s correct, so maybe there is something worng with other parts of my code. Thank you for your time.