You haven’t provided enough details for a definitive diagnosis. However,
- After CVX has solved or inaccurate/solved, the CVX variables have their optimal values. But CVX expressions do not necessarily.correspond to the optimal values of CVX variables. CVX makes sure the expressions are properly evaluated for purposes of conducting the opttimization and populating cvx_optbval, but the numerical values of CVX expressions after CVX completes do not necessarily correspond to the optimal values of the variables. Therefore, you should recompute CVX expression values using the optimal values of CVX variables if you wish to know the optimal values of CVX expressions.
- The solvers employed by CVX numerically solve the optimization problem to within a solver tolerance, to include a feasibility tolerance. Therefore, the constraints might be slightly violated even at the optimum. In your case, this could be exacerbated due to a poorly scaled problem, as evidenced by the optimal objective value being greater than 1e6, which perhaps contributed to Status being Inaccurate/Solved instead of Solved.
Given use of the CVX Successive Approximation method, I recommend you 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