I am using CVX to solve an SDP problem. CVX fails to solve the problem and shows an error msg " lack of progress in infeas ". The matlab output I am getting are as follows
----------------------------------------Output-----------------------------------------------------
Calling SDPT3 4.0: 18 variables, 10 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
num. of constraints = 10
dim. of sdp var = 6, num. of sdp blk = 2
dim. of socp var = 6, num. of socp blk = 1
SDPT3: Infeasible path-following algorithms
version predcorr gam expon scale_data
HKM 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
0|0.000|0.000|3.4e+00|8.7e+00|6.1e+02| 2.000000e+01 0.000000e+00| 0:0:00| chol 1 1
1|0.989|1.000|3.7e-02|9.6e-02|2.4e+01| 1.706179e+01 -1.224551e+00| 0:0:00| chol 1 1
2|0.989|0.996|4.1e-04|1.7e-02|6.7e-01|-4.709268e-01 -1.076886e+00| 0:0:00| chol 1 1
3|0.965|0.987|1.4e-05|1.3e-03|2.3e-02|-1.063321e+00 -1.084105e+00| 0:0:00| chol 1 1
4|1.000|1.000|4.1e-05|9.9e-05|8.9e-03|-1.078651e+00 -1.081513e+00| 0:0:00| chol 1 1
5|0.869|0.745|1.7e-05|3.7e-05|2.0e-03|-1.078973e+00 -1.076262e+00| 0:0:00| chol 1 1
6|1.000|0.941|1.4e-05|6.5e-06|7.2e-04|-1.078620e+00 -1.072879e+00| 0:0:00| chol 1 1
7|0.628|1.000|1.1e-05|2.9e-06|3.9e-04|-1.077274e+00 -1.072026e+00| 0:0:00| chol 1 1
8|1.000|1.000|1.1e-05|2.2e-06|1.6e-04|-1.077390e+00 -1.070427e+00| 0:0:00| chol 1 1
9|0.676|0.964|9.2e-06|2.3e-06|1.6e-04|-1.076066e+00 -1.068594e+00| 0:0:00| chol 1 1
10|0.020|0.495|9.0e-06|3.0e-06|4.8e-03|-1.075725e+00 -1.058955e+00| 0:0:00| chol 1 1
11|0.788|0.287|1.9e-06|4.0e-06|3.9e-02|-1.034670e+00 -1.072933e+00| 0:0:00| chol 1 1
12|0.309|0.654|1.3e-06|1.8e-06|2.9e-02|-1.039484e+00 -1.059514e+00| 0:0:00|
lack of progress in infeas
number of iterations = 12
primal objective value = -1.07606623e+00
dual objective value = -1.06859448e+00
gap := trace(XZ) = 1.57e-04
relative gap = 4.99e-05
actual relative gap = -2.38e-03
rel. primal infeas (scaled problem) = 9.23e-06
rel. dual " " " = 2.30e-06
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 1.5e+00, 3.9e+02, 3.9e+02
norm(A), norm(b), norm© = 6.0e+00, 3.0e+00, 2.8e+00
Total CPU time (secs) = 0.15
CPU time per iteration = 0.01
termination code = 0
DIMACS: 9.2e-06 0.0e+00 3.2e-06 0.0e+00 -2.4e-03 5.0e-05
Status: Solved
Optimal value (cvx_optval): +0.0685945
----------------------------------------------------end----------------------------------------------
However, when I am multiplying the objective function by 10^4 cvx is able to solve the SDP accurately. Then the output is
-----------------------------------output------------------------------------------------
Calling SDPT3 4.0: 18 variables, 10 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
num. of constraints = 10
dim. of sdp var = 6, num. of sdp blk = 2
dim. of socp var = 6, num. of socp blk = 1
SDPT3: Infeasible path-following algorithms
version predcorr gam expon scale_data
HKM 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime
0|0.000|0.000|3.0e+00|8.7e+00|3.6e+06| 1.200060e+05 0.000000e+00| 0:0:00| chol 1 1
1|0.988|0.983|3.5e-02|6.1e-01|2.4e+05| 8.834179e+04 -5.342719e+03| 0:0:00| chol 1 1
2|0.979|1.000|7.2e-04|2.4e-01|2.3e+04| 4.025289e+03 -8.566728e+03| 0:0:00| chol 1 1
3|0.981|1.000|1.4e-05|1.2e-01|9.6e+02|-1.011400e+04 -9.530978e+03| 0:0:00| chol 1 1
4|0.624|1.000|5.3e-06|6.0e-02|4.2e+02|-1.048841e+04 -1.015833e+04| 0:0:00| chol 1 1
5|0.215|0.195|4.2e-06|5.4e-02|3.7e+02|-1.042035e+04 -1.000887e+04| 0:0:00| chol 1 1
6|0.414|0.436|2.5e-06|3.7e-02|2.5e+02|-1.042433e+04 -1.006334e+04| 0:0:00| chol 1 1
7|0.305|0.441|1.7e-06|2.4e-02|2.2e+02|-1.038446e+04 -1.007869e+04| 0:0:00| chol 1 1
8|0.285|0.792|1.2e-06|8.0e-03|2.2e+02|-1.033242e+04 -1.012363e+04| 0:0:00| chol 1 1
9|0.446|1.000|6.8e-07|1.9e-03|2.1e+02|-1.022707e+04 -1.015190e+04| 0:0:00| chol 1 1
10|0.746|0.820|1.7e-07|1.1e-03|7.3e+01|-1.011609e+04 -1.007428e+04| 0:0:00| chol 1 1
11|0.309|1.000|1.2e-07|4.7e-04|6.4e+01|-1.009341e+04 -1.003637e+04| 0:0:00| chol 1 1
12|0.776|0.709|2.7e-08|3.0e-04|2.7e+01|-1.002348e+04 -1.001166e+04| 0:0:00| chol 1 1
13|0.619|0.680|1.0e-08|1.8e-04|1.4e+01|-1.000872e+04 -1.000322e+04| 0:0:00| chol 1 1
14|0.708|0.844|3.0e-09|7.7e-05|7.1e+00|-1.000084e+04 -1.000048e+04| 0:0:00| chol 1 1
15|0.910|1.000|2.7e-10|2.9e-05|2.6e+00|-9.998592e+03 -1.000021e+04| 0:0:00| chol 1 1
16|1.000|1.000|3.7e-14|1.5e-05|5.8e-01|-9.999514e+03 -9.999941e+03| 0:0:00| chol 1 1
17|0.845|1.000|1.1e-14|5.3e-12|1.2e-01|-9.999905e+03 -1.000003e+04| 0:0:00| chol 1 1
18|1.000|0.972|6.5e-15|5.4e-12|3.3e-02|-9.999971e+03 -1.000000e+04| 0:0:00| chol 1 1
19|0.828|1.000|3.3e-15|2.8e-12|7.7e-03|-9.999995e+03 -1.000000e+04| 0:0:00| chol 1 1
20|1.000|0.915|5.5e-15|2.8e-12|2.1e-03|-9.999998e+03 -1.000000e+04| 0:0:00| chol 1 1
21|0.858|1.000|2.2e-15|8.5e-13|3.3e-04|-1.000000e+04 -1.000000e+04| 0:0:00| chol 1 1
22|1.000|0.883|2.9e-15|2.8e-12|1.0e-04|-1.000000e+04 -1.000000e+04| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-08
number of iterations = 22
primal objective value = -9.99999991e+03
dual objective value = -1.00000000e+04
gap := trace(XZ) = 1.00e-04
relative gap = 5.02e-09
actual relative gap = 5.02e-09
rel. primal infeas (scaled problem) = 2.91e-15
rel. dual " " " = 2.80e-12
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 1.4e+04, 1.4e+05, 8.8e+04
norm(A), norm(b), norm© = 6.0e+00, 2.0e+04, 2.8e+00
Total CPU time (secs) = 0.20
CPU time per iteration = 0.01
termination code = 0
DIMACS: 2.9e-15 0.0e+00 3.9e-12 0.0e+00 5.0e-09 5.0e-09
Status: Solved
Optimal value (cvx_optval): +1.2115e-05
--------------------------------------------end----------------------------------------------------------------------
Please help me to understand why it is happening. Thankyou