i'm trying to solve this constrained optimization problem
the constraint is $$\zeta=\frac {\Gamma \left(M,\frac {\lambda}{\left |\sum_{i=1}^Nw_i*h_{ei} \right|^2 + \sum_{i=1}^N\left |w_i \right|^2} \right)}{\Gamma(M)}*\beta +\frac {\Gamma \left(M,\frac {\lambda}{\sum_{i=1}^N \left |w_i \right|^2} \right)}{\Gamma(M)}*(1-\beta)$$
and the fitness function is
$$P_d=\frac {\Gamma \left(M,\frac {\lambda}{\left |\sum_{i=1}^Nw_i*h_{pi} \right|^2+\left |\sum_{i=1}^Nw_i*h_{ei} \right|^2 + \sum_{i=1}^N\left |w_i \right|^2} \right)}{\Gamma(M)}*\alpha +\frac {\Gamma \left(M,\frac {\lambda}{\left |\sum_{i=1}^Nw_i*h_{pi} \right|^2 + \sum_{i=1}^N\left |w_i \right|^2} \right)}{\Gamma(M)}*(1-\alpha)$$
where $\Gamma(M,...)$ is upper incomplete gamma function. it is notable that $h_{pi}$ and $w_i$ are complex variables
in the above equations $\zeta$, $M$, $N$, $\beta$, $\alpha$, $\lambda$, $h_{pi}$ for(i=1,...,N) and $h_{ei}$ for(i=1,...,N) are known.
the parameters of our optimization problem are $\lambda$ and $w_i$ for (i=1,...,N) and the fitness function is $P_d$
this problem is from my telecommunication model
pleas guide me to solve this constrained optimization problem
2026-04-04 22:38:12.1775342292