How to handle the constraint involving perspective functions $\left( \exp\left(\beta y \oslash x \right) - 1 \right)$

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I also recommend you follow the advice in 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