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I would like to solve the following optimization problem:

$$ \max\{\min_{k=1,2,...,m}\{R_d^k\}+\sum_{k=1}^m R_e^k\} \\\text{s.t.} \\ \mathrm{trace}(W_d^kW_d^{kT})=1 \\ \mathrm{trace}(W_e^kW_e^{kT})=1 \\0<P_d^k<P_d^{Max} \\0<P_e^k<P_e^{Max} $$

where

  • $R_d^k$ and $R_e^k$ are both non-linear, non-convex functions of variables $W_d^k$, $W_e^k$, $P_d^k$, and $P_e^k$,
  • $W_d^k$ and $W_e^k$ are 2-by-2 matrices, and
  • $P_d^k$ and $P_e^k$ are scalar values.

What method can I use to solve this problem?

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