Fmincon optimization for complex vectors

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yasser
yasser 2016-1-30
评论： yasser 2016-2-3
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

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回答（1 个）

Walter Roberson
Walter Roberson 2016-1-31
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)

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