I applied CVX to solve some academic research problems. There were some errors in the CVX program I wrote. I hope I can get your help

## This is the result of my program

Successive approximation method to be employed.

For improved efficiency, SDPT3 is solving the dual problem.

SDPT3 will be called several times to refine the solution.

Original size: 13 variables, 4 equality constraints

1 exponentials add 8 variables, 5 equality constraints

## Cones | Errors |

Mov/Act | Centering Exp cone Poly cone | Status

--------±--------------------------------±--------

1/ 1 | 5.957e+00 8.600e+00 0.000e+00 | Failed

1/ 1 | 3.712e-01 1.166e-02 0.000e+00 | Solved

1/ 1 | 5.631e-02 2.602e-04 0.000e+00 | Solved

1/ 1 | 7.236e-03 4.256e-06 0.000e+00 | Solved

1/ 1 | 9.074e-04 3.453e-08 0.000e+00 | Solved

0/ 0 | 1.133e-04 0.000e+00 0.000e+00 | Solved

Status: Solved

Optimal value (cvx_optval): -776.199

## The following is a very good CVX example

Calling SDPT3 4.0: 17 variables, 9 equality constraints

For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 9

dim. of socp var = 17, num. of socp blk = 1

SDPT3: Infeasible path-following algorithms

## version predcorr gam expon scale_data

NT 1 0.000 1 0

it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

## 0|0.000|0.000|1.6e+00|1.4e+00|2.1e+01| 0.000000e+00 0.000000e+00| 0:0:00| chol 1 1

1|1.000|1.000|2.8e-06|2.2e-02|2.2e+00|-1.541481e+00 -3.662905e+00| 0:0:00| chol 1 1

2|1.000|0.959|5.1e-08|3.0e-03|7.4e-02|-1.961811e+00 -2.021858e+00| 0:0:00| chol 1 1

3|0.988|0.988|1.2e-08|2.6e-04|9.0e-04|-2.003281e+00 -2.003023e+00| 0:0:00| chol 1 1

4|0.989|0.989|1.0e-08|2.5e-05|9.9e-06|-2.003785e+00 -2.003684e+00| 0:0:00| chol 1 1

5|0.990|0.990|1.8e-10|2.6e-07|1.2e-07|-2.003791e+00 -2.003790e+00| 0:0:00| chol 1 1

6|0.990|0.990|2.7e-12|2.7e-09|1.4e-09|-2.003791e+00 -2.003791e+00| 0:0:00|

stop: max(relative gap, infeasibilities) < 1.49e-08

## number of iterations = 6

primal objective value = -2.00379086e+00

dual objective value = -2.00379085e+00

gap := trace(XZ) = 1.43e-09

relative gap = 2.85e-10

actual relative gap = -2.12e-09

rel. primal infeas (scaled problem) = 2.67e-12

rel. dual " " " = 2.66e-09

rel. primal infeas (unscaled problem) = 0.00e+00

rel. dual " " " = 0.00e+00

norm(X), norm(y), norm(Z) = 1.4e+00, 2.6e+00, 2.8e+00

norm(A), norm(b), norm© = 1.2e+01, 2.0e+00, 4.5e+00

Total CPU time (secs) = 0.09

CPU time per iteration = 0.02

termination code = 0

DIMACS: 2.7e-12 0.0e+00 4.7e-09 0.0e+00 -2.1e-09 2.8e-10

Status: Solved

Optimal value (cvx_optval): +2.00379

Obviously, the two results are a little different. My is not quite correct. Why? If you need, I can provide you with my source program.