Fmincon optimization for complex vectors

I'm having an optimization problem where the objective function and the constraints have log terms , the optimization variable is a 2d complex vector

When using fmincon I get an error that implies that optimizing over a complex variable is not allowed in fmincon

The problem is

Max log2(abs(h1*w(1))) st log2(abs(h2*w(2)))<epsilon

The optimization vector is w

Thanks

Answer 1

[Walter Roberson]

Break each optimization variable up into two pieces, one for the real part, one for the imaginary part:

function w4 = opt_driver(h1, h2)

     obj = @(w) -objective(w, h1, h2);
     nl = @(w) nonlcon(w, h1, h2);
     w4 = fmincon(obj, [], [], [], [], nl);

function [c, ceq] = nonlcon(w, h1, h2)
  ceq = [];
  %positive value means the constraint is violated
  c = log2(abs(h2* (w(3)+1i*w(4)) )) >= epsilon;

function f = objective(w, h1, h2)
   f = log2(abs(h1* (w(1)+1i*w(2)) ));

The result would be a vector of 4 real values, with your w(1) being w4(1)+1i*w4(2) and your w(2) being w4(3)+1i*w4(4)

[yasser]

Thanks for your care and sorry for late reply