Here is my variable definition related to the unsatisfied constraint it is a three dimension tensor.

variable R_User_o(RRH_Num * RRH_Ant,RRH_Num * RRH_Ant,UE_Num) complex

Here is the unsatisfied constraint

for ue = 1 : UE_Num

(1 + Tau^-1) * real( Int_Cha(ue,: ) * R_User_o(:,:,ue) * Int_Cha(ue,: )’ ) - real( Int_Cha(ue,: ) * R_Int_o * Int_Cha(ue,: )’ ) - n_sigma >= 10^-100;

R_User_o(:,:,ue) == hermitian_semidefinite(RRH_Num * RRH_Ant);

end

except the optimization variable, other variables are pre-computed.

In my verification

denominator = real( Int_Cha(ue,: ) * R_Int_o * Int_Cha(ue,:)’ ) + n_sigma

ans = (1 + Tau^-1) * real( Int_Cha(ue,: ) * R_User_o(:,:,ue) * Int_Cha(ue,:)’ ) Tau equals to 2.5119

The first two computation result seriously violates the constraint. Only the last one just meet the equal constraint I mark it as 3 means it meet the constraint.

Here is the Mosek Result

CVX Warning:

Models involving “log_det” or other functions in the log, exp, and entropy

family are solved using an experimental successive approximation method.

This method is slower and less reliable than the method CVX employs for

other models. Please see the section of the user’s guide entitled

The successive approximation method

for more details about the approach, and for instructions on how to

suppress this warning message in the future.

## Calling Mosek 9.1.9: 432 variables, 203 equality constraints

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 : 203

Cones : 44

Scalar variables : 174

Matrix variables : 8

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: 0.01

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 203

Cones : 44

Scalar variables : 174

Matrix variables : 8

Integer variables : 0

Optimizer - threads : 12

Optimizer - solved problem : the primal

Optimizer - Constraints : 129

Optimizer - Cones : 45

Optimizer - Scalar variables : 139 conic : 134

Optimizer - Semi-definite variables: 8 scalarized : 510

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 : 4649 after factor : 4777

Factor - dense dim. : 0 flops : 7.05e+05

ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME

0 2.6e+01 1.3e+00 2.2e+01 0.00e+00 1.000000000e+00 -1.961020400e+01 1.0e+00 0.01

1 8.4e+00 4.2e-01 1.1e+01 -8.53e-01 3.013684725e+00 -1.359169440e+01 3.3e-01 0.08

2 3.0e+00 1.5e-01 5.1e+00 -6.61e-01 9.322791442e+00 -1.257534399e+00 1.2e-01 0.08

3 1.5e+00 7.4e-02 2.5e+00 -3.31e-01 1.946250927e+01 1.287361393e+01 5.7e-02 0.08

4 4.8e-01 2.4e-02 5.0e-01 2.41e-01 3.743737781e+01 3.476971661e+01 1.9e-02 0.08

5 2.3e-01 1.2e-02 1.7e-01 8.81e-01 4.335199229e+01 4.206682821e+01 9.0e-03 0.09

6 1.5e-01 7.7e-03 1.0e-01 5.54e-01 4.704248991e+01 4.614311000e+01 5.9e-03 0.09

7 6.5e-02 3.3e-03 2.9e-02 8.73e-01 5.014858520e+01 4.975616869e+01 2.6e-03 0.09

8 1.7e-02 8.6e-04 3.4e-03 1.21e+00 4.718953303e+01 4.709222359e+01 6.7e-04 0.09

9 4.4e-03 2.2e-04 4.8e-04 1.14e+00 4.491014082e+01 4.488904362e+01 1.7e-04 0.09

10 6.8e-04 3.4e-05 2.9e-05 1.01e+00 4.452600773e+01 4.452289238e+01 2.7e-05 0.09

11 2.8e-04 1.4e-05 8.0e-06 9.15e-01 4.450032026e+01 4.449905197e+01 1.1e-05 0.09

12 1.1e-04 5.6e-06 2.1e-06 9.24e-01 4.448604284e+01 4.448553140e+01 4.3e-06 0.11

13 6.8e-05 3.4e-06 1.1e-06 8.54e-01 4.448455223e+01 4.448423510e+01 2.7e-06 0.11

14 2.5e-05 1.3e-06 2.5e-07 9.21e-01 4.448049517e+01 4.448037676e+01 9.8e-07 0.11

15 1.1e-05 5.6e-07 8.2e-08 8.24e-01 4.448037023e+01 4.448031973e+01 4.3e-07 0.11

16 1.6e-06 8.0e-08 4.5e-09 9.50e-01 4.447936217e+01 4.447935509e+01 6.2e-08 0.11

17 1.6e-07 2.1e-08 1.4e-10 9.96e-01 4.447921730e+01 4.447921660e+01 6.0e-09 0.11

18 4.5e-09 4.5e-09 5.7e-13 1.00e+00 4.447920369e+01 4.447920368e+01 1.5e-10 0.13

Optimizer terminated. Time: 0.16

Interior-point solution summary

Problem status : PRIMAL_AND_DUAL_FEASIBLE

Solution status : OPTIMAL

Primal. obj: 4.4479203695e+01 nrm: 3e+02 Viol. con: 2e-07 var: 0e+00 barvar: 0e+00 cones: 0e+00

Dual. obj: 4.4479203676e+01 nrm: 5e+01 Viol. con: 0e+00 var: 1e-10 barvar: 3e-10 cones: 3e-16

Optimizer summary

Optimizer - time: 0.16

Interior-point - iterations : 18 time: 0.13

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: Solved

Optimal value (cvx_optval): +44.4792

Does the problem has something to do with scaling?? or other reasons. Thank you very much.