How to express log(trace(AX)+b) in CVX

[Kevin3 (Kevin)]

Hi Mark, how to express log(trace(AX)+b) in CVX. I am expression it directly in cvx, but not sure whether it violet the cvx rule.

[NWPU_Xiu]

As I know, if you express it directly in cvx, the cvx may give some warings. It doesn’t mean you are wrong.
You can use the ‘rel_entr’ function.
You can check this:

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

How to use CVXQUAD’s better performing and more reliable Pade Approximant instead of CVX’s unreliable Successive Approximation method: Note: Except for use of Quantum (Matrix) Entropy and Matrix Logarithm related functions addressed later in this post, none of the following, to include reformulation, is necessary if CVX 2.2 is used with Mosek 9.x as solver, in which case CVX will utilize Mosek 9.x’s native exponential cone capability, thereby avoiding CVX"s Successive Approximation method and o…

[Kevin3 (Kevin)]

so, I should use like this rel_entr(trace(A*X)+b) ? I am not sure.

[NWPU_Xiu]

Replace
log(cvx_expression)
with
-rel_entr(1,cvx_expresion)

[Kevin3 (Kevin)]

Nice, thank you very much .

[Mark_L_Stone]

You can enter it in CVX directly as
log(trace(A*X)+b)

If you, use CVX 2.2 and have available Mosek as solver, this suffices. In such case, you can use -rel_entr(1,trace(A*X)+b) instead of log(trace(A*X)+b), but it is just an unnecessary reduction in the understandability of the code.

If you do not have Mosek available as solver, then you should use -rel_entr(1,trace(A*X)+b) and install CVXQUAD’s exponential.m replacement as described in the link provided by @NWPU_Xiu

[Kevin3 (Kevin)]

Thank you very much Mark.