(Help) How can I deal with this SDR problem?

1

This SDR problem comes from someone else paper, and i wand use matlab to solve it. Here is the problem:

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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?

2

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.

3

Thank you so much for your advice and reference. I will figure it out, thanks.