Thank you for MOSEK suggestion.

I tried solving my problem with MOSEK, the problem is infeasible.

This is the result, I obtained from MOSEK.

Problem

Name :

Objective sense : min

Type : CONIC (conic optimization problem)

Constraints : 49

Cones : 1

Scalar variables : 304

Matrix variables : 0

Integer variables : 0

Optimizer started.

Conic interior-point optimizer started.

Presolve started.

Linear dependency checker started.

Linear dependency checker terminated.

Eliminator started.

Freed constraints in eliminator : 3

Eliminator terminated.

Eliminator started.

Freed constraints in eliminator : 3

Eliminator terminated.

Eliminator - tries : 2 time : 0.00

Lin. dep. - tries : 1 time : 0.00

Lin. dep. - number : 0

Presolve terminated. Time: 0.02

Optimizer - threads : 4

Optimizer - solved problem : the primal

Optimizer - Constraints : 43

Optimizer - Cones : 2

Optimizer - Scalar variables : 173 conic : 41

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 : 946 after factor : 946

Factor - dense dim. : 0 flops : 3.44e+004

ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME

0 1.0e+000 6.6e+004 1.0e+000 0.00e+000 4.950000000e+004 4.950000000e+004 1.0e+000 0.03

1 5.0e-001 3.3e+004 3.5e-001 -1.00e+000 4.534838583e+004 4.949440557e+004 5.0e-001 0.06

2 1.5e-001 9.8e+003 5.7e-002 -1.00e+000 2.590700549e+004 4.950026027e+004 1.5e-001 0.06

3 8.4e-002 5.6e+003 2.5e-002 -9.99e-001 5.087157063e+003 4.949103909e+004 8.4e-002 0.06

4 2.2e-002 1.5e+003 3.3e-003 -9.97e-001 -1.293073763e+005 4.945655873e+004 2.2e-002 0.06

5 3.6e-003 2.3e+002 2.2e-004 -9.79e-001 -9.886990234e+005 4.917080361e+004 3.6e-003 0.08

6 3.9e-004 2.5e+001 1.1e-005 -8.27e-001 -4.697540269e+006 4.740080116e+004 3.9e-004 0.08

7 5.7e-006 3.8e-001 2.2e-007 -4.97e-002 -2.723911672e+006 4.507339733e+004 5.7e-006 0.08

8 2.5e-006 1.6e-001 1.8e-007 1.26e+000 -7.034301668e+005 4.502750169e+004 2.5e-006 0.08

9 1.2e-006 7.9e-002 1.4e-007 1.12e+000 -2.742235425e+005 4.501350446e+004 1.2e-006 0.08

10 2.8e-007 1.8e-002 7.5e-008 1.11e+000 -1.158147576e+004 4.500285050e+004 2.8e-007 0.09

11 1.3e-007 8.8e-003 4.2e-008 7.25e-001 3.184764236e+003 4.500176963e+004 1.3e-007 0.09

12 2.4e-008 1.6e-003 2.4e-009 -1.72e-001 -3.627929302e+005 4.500421625e+004 2.4e-008 0.09

13 2.0e-010 1.3e-005 2.9e-012 -7.85e-001 -2.322515701e+007 4.500223305e+004 2.0e-010 0.09

14 1.6e-012 6.5e-008 2.6e-012 -9.99e-001 -9.055357412e+000 -4.458621635e-009 2.9e-016 0.09

Interior-point optimizer terminated. Time: 0.09.

MOSEK DUAL INFEASIBILITY REPORT.

Problem status: The problem is dual infeasible

Optimizer terminated. Time: 0.14

Interior-point solution summary

Problem status : DUAL_INFEASIBLE

Solution status : DUAL_INFEASIBLE_CER

Primal. obj: -9.0553574022e+000 nrm: 2e+003 Viol. con: 3e-008 var: 0e+000 cones: 0e+000

Optimizer summary

Optimizer - time: 0.14

Interior-point - iterations : 14 time: 0.09

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: Infeasible

Optimal value (cvx_optval): +Inf

Elapsed time is 0.924060 seconds.