Your problem appears to be unbounded, at least with the two sets of random numbers I generated.

Mosek reported primal infeasible or unbounded with solution status UNKNOWN. Mosek was provided the dual problem by CVX, and CVX provided the status Failed (with or without the cvx_solver_settings in your code).

I then removed the binary declaration and constrained all of what were the binary variables to all zeros. Mosek (which was provided the dual by CVX), reported primal infeasible, which resulted in CVX providing status (primal) unbounded. The same CVX status of unbounded occurred when I ran this same modified program in SeDuMi and SDPT3. Even reducing M to 1 (or even 0) from 1e3 had the same outcome. Even the continuous relaxation of the binaries to [0,1] resulted in unbounded. If the problem is unbounded with binary variables constrained to zero, then the original problem must also be unbounded - I merely helped out the solver.

Try following the advice at https://yalmip.github.io/debuggingunbounded , which also applies to CVX.

I will defer to the Mosek people to provide any further commentary or assessment.

Below I show (for one common set of random numbers) the Mosek output, first from the code as in your post, and then when I removed the binary declarations and constrained those variables to all zeros:

Code as posted:

## Calling Mosek 9.3.6: 374 variables, 239 equality constraints

MOSEK Version 9.3.7 (Build date: 2021-10-11 10:42:47)

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

Platform: Windows/64-X86

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 239

Cones : 3

Scalar variables : 374

Matrix variables : 0

Integer variables : 34

Optimizer started.

Mixed integer optimizer started.

Threads used: 8

Presolve started.

Presolve terminated. Time = 0.00

Presolved problem: 81 variables, 80 constraints, 259 non-zeros

Presolved problem: 0 general integer, 26 binary, 55 continuous

Clique table size: 0

BRANCHES RELAXS ACT_NDS DEPTH BEST_INT_OBJ BEST_RELAX_OBJ REL_GAP(%) TIME

0 0 1 0 0.0000000000e+00 NA NA 0.1

0 1 1 0 0.0000000000e+00 NA NA 0.1

Objective of best integer solution : 0.000000000000e+00

Best objective bound : 0.000000000000e+00

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: 0

Number of simplex iterations : 0

Time spend presolving the root : 0.00

Time spend optimizing the root : 0.00

Mixed integer optimizer terminated. Time: 0.14

Optimizer terminated. Time: 0.20

Integer solution solution summary

Problem status : PRIMAL_INFEASIBLE_OR_UNBOUNDED

Solution status : UNKNOWN

Primal. obj: 0.0000000000e+00 nrm: 1e+03 Viol. con: 0e+00 var: 0e+00 cones: 0e+00 itg: 0e+00

Optimizer summary

Optimizer - time: 0.20

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: 0.14

Status: Failed

Optimal value (cvx_optval): NaN

++++++++++++++++++++++++++++++++++++++++++

When removed the binary declarations and constrained those variables to all zeros:

## Calling Mosek 9.3.6: 263 variables, 101 equality constraints

For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.3.7 (Build date: 2021-10-11 10:42:47)

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

Platform: Windows/64-X86

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 101

Cones : 3

Scalar variables : 263

Matrix variables : 0

Integer variables : 0

Optimizer started.

Presolve started.

Eliminator - tries : 0 time : 0.00

Lin. dep. - tries : 0 time : 0.00

Lin. dep. - number : 0

Presolve terminated. Time: 0.00

Optimizer terminated. Time: 0.09

Interior-point solution summary

Problem status : PRIMAL_INFEASIBLE

Solution status : PRIMAL_INFEASIBLE_CER

Dual. obj: 1.0000000000e+06 nrm: 8e+06 Viol. con: 0e+00 var: 0e+00 cones: 0e+00

Optimizer summary

Optimizer - time: 0.09

Interior-point - iterations : 0 time: 0.03

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: 0 time: 0.00

Status: Unbounded

Optimal value (cvx_optval): +Inf