Is the final result of CVX reliable when the Status is failed?

The result is not failed. That is the status of an iteration of CVX"s Successive Approximation method. The result is Inaccurate Solved, which might be a valid solution, but not very accurate.

In order to more reliably and accrrately solve the problem:
If you have access to Mosek 9.x, use that with CVX 2.2. II not, follow the directions 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 .

I see from your posting history that you were aware of CVXQUAD two years ago, so I am a little surprised you were not using it (at least properly) for this problem.

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