Here is my optimization problem, which is linear and convex, But when I use cvx to solve it, it always fails. I think the gap is 10^(-4), not so large, and I get the solutions to the variables even if it shows to be failed and NAN, why is it that? Is it because that the variables are too many or too many constraints?
Calling SDPT3 4.0: 3003 variables, 600 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.
num. of constraints = 600
dim. of linear var = 2860
dim. of free var = 143
462 linear variables from unrestricted variable.
*** convert ublk to lblk
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|4.3e+07|5.0e+01|2.1e+10| 1.316889e+08 0.000000e+00| 0:0:00| spchol 2 2
1|0.755|0.539|1.1e+07|2.3e+01|1.2e+10| 4.058411e+07 -1.532496e+03| 0:0:00| spchol 1 1
2|0.838|0.862|1.7e+06|3.2e+00|1.9e+09| 1.088092e+07 -3.398017e+02| 0:0:00| spchol 1 1
3|0.951|0.958|8.4e+04|1.3e-01|8.1e+07| 1.910512e+06 -1.390760e+01| 0:0:00| spchol 1 1
4|0.678|0.073|2.7e+04|1.2e-01|9.2e+07| 9.086600e+05 -1.284250e+01| 0:0:00| spchol 1 1
5|0.701|0.400|8.1e+03|7.4e-02|6.1e+07| 5.362101e+05 -7.708055e+00| 0:0:00| spchol 1 1
6|0.432|0.267|4.6e+03|5.4e-02|4.8e+07| 4.679443e+05 -5.533952e+00| 0:0:00| spchol 1 1
7|0.357|0.167|3.0e+03|4.5e-02|4.2e+07| 4.415070e+05 -4.593566e+00| 0:0:00| spchol 1 1
8|0.485|0.214|1.5e+03|3.5e-02|3.6e+07| 4.195032e+05 -3.520497e+00| 0:0:00| spchol 1 1
9|0.930|0.230|1.1e+02|2.7e-02|3.2e+07| 3.922352e+05 -2.653331e+00| 0:0:00| spchol 1 1
10|0.999|0.946|1.6e-01|1.5e-03|2.0e+06| 3.446933e+05 2.175657e-01| 0:0:00| spchol 1 1
11|1.000|0.058|7.4e-07|1.4e-03|2.0e+06| 2.530785e+05 2.257479e-01| 0:0:00| spchol 1 1
12|1.000|0.602|1.8e-04|5.5e-04|8.6e+05| 1.891638e+05 3.172082e-01| 0:0:00| spchol 1 1
13|1.000|0.354|4.2e-05|3.6e-04|5.2e+05| 1.139091e+05 3.378239e-01| 0:0:00| spchol 1 1
14|1.000|0.276|4.2e-05|2.6e-04|4.0e+05| 8.308469e+04 3.484246e-01| 0:0:00| spchol 1 1
15|1.000|0.359|4.8e-05|1.7e-04|2.7e+05| 5.952155e+04 3.580096e-01| 0:0:00| spchol 1 1
16|1.000|0.480|4.4e-05|8.7e-05|1.4e+05| 2.864650e+04 3.671097e-01| 0:0:00| spchol 1 1
17|1.000|0.573|3.1e-05|3.8e-05|6.0e+04| 1.120950e+04 3.737165e-01| 0:0:00| spchol 1 1
18|0.993|0.831|1.8e-05|7.1e-06|1.1e+04| 1.610452e+03 3.830029e-01| 0:0:00| spchol 1 1
19|0.960|0.850|3.2e-05|1.2e-06|1.9e+03| 4.117588e+02 4.278137e-01| 0:0:00| spchol 1 1
20|0.849|0.878|1.1e-05|1.6e-07|2.9e+02| 7.556815e+01 5.997852e-01| 0:0:00| spchol 2 2
21|1.000|0.314|1.2e-05|1.3e-07|1.8e+02| 1.478241e+01 6.984050e-01| 0:0:00| spchol 2 2
22|1.000|0.574|5.5e-05|5.9e-08|8.5e+01| 5.619081e+00 8.304684e-01| 0:0:00| spchol 2 2
23|1.000|0.909|1.2e-05|5.9e-09|8.2e+00| 1.080248e+00 9.259104e-01| 0:0:00| spchol 2 2
24|0.929|0.981|5.5e-06|1.3e-10|1.8e-01| 9.460832e-01 9.354486e-01| 0:0:01| spchol
SMW too ill-conditioned, switch to LU factor, 5.8e+20. splu 5 1
25|1.000|0.186|4.3e-05|2.3e-09|1.7e-01| 9.381924e-01 9.354819e-01| 0:0:01| splu 18 1
26|1.000|0.915|1.7e-04|3.3e-09|3.1e-02| 9.443428e-01 9.355946e-01| 0:0:01| splu 18 1
27|0.949|0.901|9.1e-06|6.1e-10|3.1e-03| 9.361422e-01 9.356332e-01| 0:0:01| splu 11 ^ 7
28|0.000|0.000|9.1e-06|6.1e-11|2.6e-03| 9.361406e-01 9.356332e-01| 0:0:01| splu 39 ^ 3
29|0.000|0.000|9.2e-06|5.1e-11|2.8e-03| 9.361418e-01 9.356332e-01| 0:0:01|
stop: progress is bad
stop: steps too short consecutively
number of iterations = 29
primal objective value = 9.36140567e-01
dual objective value = 9.35633171e-01
gap := trace(XZ) = 2.56e-03
relative gap = 8.90e-04
actual relative gap = 1.77e-04
rel. primal infeas (scaled problem) = 9.08e-06
rel. dual " " " = 6.10e-11
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 1.5e+07, 5.2e+01, 1.5e+05
norm(A), norm(b), norm© = 3.2e+05, 1.6e+00, 1.6e+05
Total CPU time (secs) = 0.64
CPU time per iteration = 0.02
termination code = -5
DIMACS: 1.2e-05 0.0e+00 9.6e-10 0.0e+00 1.8e-04 8.9e-04
Status: Failed
Optimal value (cvx_optval): NaN