The CVX iteration shows:

is the output reliable？

Maybe yes, maybe no.

First, try to make sure the input data has good scaling. Then follow the advice at 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 .

When the objective function is set as “log - ( square + linear )”:

the CVX cannot solve the problem, and the status is unbounded.

While it’s set as “log - ( linear )”:

the status is solved.

I want to know if CVX can’t solve the problem like “log - ( square + linear )” ?

Check you input data scaling.

Them follow the advice at https://yalmip.github.io/debuggingunbounded .

Is that mean if I have an appropriate input, CVX can solve the problem better perhaps?

Everything depends on the combination of model, input data, and solver.

Do you know what will happen with this problem?

`cvx_begin;variable x;minimize(x);cvx_end`

It will be declared unbounded.

Do you know what will happen to this problem?

`cvx_begin;variable x;minimize(x);x >= 1; cvx_end`

It will be solved to optimality.

OK, maybe I know. Thank you Mark~