rng("default")
n = 32;
y = rand(n,1) + 1i*rand(n,1);
B = rand(n) + 1i*rand(n);
x0 = rand(n,1) + 1i*rand(n,1);
x0 = [real(x0);imag(x0)];
x0 = x0./[sqrt(x0(1:n).^2+x0(n+1:2*n).^2);sqrt(x0(1:n).^2+x0(n+1:2*n).^2)];
fun = @(x)(B*(x(1:n)+1i*x(n+1:2*n))-y)'*(B*(x(1:n)+1i*x(n+1:2*n))-y);
fun(x0)
nonlcon = @(x)deal([],x(1:n).^2+x(n+1:2*n).^2-ones(n,1));
sol = fmincon(fun,x0,[],[],[],[],[],[],nonlcon,optimset('MaxFunEvals',10000,'TolFun',1e-12,'TolX',1e-12))
fun(sol)
sol(1:n).^2+sol(n+1:2*n).^2-ones(n,1)
