Why the constraint dosen't take effect in cvx model

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When status is failed, any returned result in meaningless.

You haven’t shown the output, so I don’t know what solution method was used. Because rel_entr is used with a CVX argument, the problem has either been solved with CVX"s Successive Approximation Method, CVXQUAD, or Mosek native exponential cone.

The best method is Mosek native exponential cone, which is automatically invoked if CVX 2,2 is used with Mosek 9.x. That is the best method.

If that is not available and CVXQUAD with exponential.m replacement is used, CVXQUAD will be used.

Otherwise, CVX"s Successive Approximation Method, which often fails, and is the worst of the methods, will be used.

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 provides instructions.

As for scaling, try to choose better units for the variables.