HELP! Why the status of the first status is often Unbounded

1

When i was trying to figure out a problem in the form of sum_m(log(Am(x)/Bm(x)）+ （penalty term） using SCA(every iterations of the problem is proved convex)， i always get the result in every iterations like:

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
40/ 40 | 8.000e+00 4.522e+00 0.000e+00 | Unbounded
60/ 60 | 8.000e+00 8.877e+00 0.000e+00 | Solved
59/ 60 | 2.706e+00 4.887e-01 0.000e+00 | Solved
58/ 60 | 1.743e-01 1.895e-03 0.000e+00 | Solved
35/ 58 | 1.989e-02 2.480e-05 0.000e+00 | Solved
20/ 29 | 2.701e-03 4.514e-07 0.000e+00 | Solved
0/ 18 | 3.751e-04 3.504e-09 0.000e+00 | Solved

Why it is always unbounded in the first line of the result?

2

By the way, i used -rel_entr(1,x) to replace the log(cvx_expression) term.

3

Don’t worry about what the first “iteration” says. Only worry about the final status reported by CVX.

In order for -rel_entr(1,x) to avoid CVX;s Successive Approximation method, you need to have CVXQUAD installed with its exponential.m replacement.

if you have Mosek available as solver, that’s even better, and no need to changelog(x) to -rel_entr(1,x) or install CVXQUAD.

See CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions

4

Really appreciate your help! I will try to use Mosek to see if i will get better results!

5

Mosek is not a magic panacea which cures all of SCA"s ills.