This SDR problem comes from someone else paper, and i wand use matlab to solve it. Here is the problem:
and this is part of my codes:
cvx_begin
variable V(N+1,N+1) symmetric
expression delta
maximize delta
subject to
for i = 1:K
trace(R_kk{i}*V) + norm(b_kk(i))^2 >= delta*(trace(R_km_sum{i}*V)) + delta*(norm(b_km_sum(i))^2 + P_noise);
end
for n=1:N+1
V(n,n) == 1;
end
V == semidefinite(N+1);
cvx_end
From the output data, I think my way is not correct, can you help me about this problem?
You haven’t told us clearly what all those symbols are, and their unstated relations.
Nevertheless, if this is a quasiconvex optimization problem to be solved by bisection, you need to call CVX within a loop, each time solving a convex feasibility problem. per the reference in my last paragraph below.
Whether you realize it or not, you are solving a single feasibility problem. That is because CVX expressions are initialized to zero. Therefore, maximize delta is treated by CVX as maximize 0, i.e., a feasibility problem. And `delta is used nowhere else in your program.
Algorithm 4.1 Bisection method for quasiconvex optimization. in Convex Optimization – Boyd and Vandenberghe shows the bisection algorithm for solving quasiconvex optimization problems.
Thank you so much for your advice and reference. I will figure it out, thanks.
