Complex {positive constant} ./ {complex affine}

Nonconvex
1

I am having an issue with the division of cvx offine//

G=sqrt(.5)*(randn((N),M)+1i*(randn((N),M)));
hau=sqrt(.5)*(randn((1),M)+1i*(randn((1),M)));
hae=sqrt(.5)*(randn((1),M)+1i*(randn((1),M)));
hiu=sqrt(.5)*(randn((1),N)+1i*(randn((1),N)));
hie=sqrt(.5)*(randn((1),N)+1i*(randn((1),N)));
theta=(2*pi)*rand(N,1);%values in radians
v=exp(1i*2*pi*theta);
theta1=diag(v);

a = 1;%var
b = 0;%mean

f= a.*(randn(M,1)+1i*randn(M,1)) + b; f=f*f';
d1=(1/sigma_u^2);
d2=(1/sigma_e^2);
A=((hiu*theta1*G+hau)'*(hiu*theta1*G+hau))*d1;A=A*A';
B=((hie*theta1*G+hae)'*(hie*theta1*G+hae))*d2;B=B*B';
cvx_begin 
variable f(M,M) symmetric
maximize(trace((f*A)+1/(f*B)+1 ))
subject to
trace(f)<=Pt;
f == semidefinite(M);
 
cvx_end
2

f*B is a matrix. So what is 1/(f*B) ? That is not defined in MATLAB. Do you mean inv(f*B)?

In any event, the expression is clear if M = N = 1, so that f*B is a scalar. In that case, because B >= 0, 1/f*B is convex, and therefore the objective is not concave, and the problem is not convex.

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