# Optimal value (cvx_optval): NaN

clear;close all;clc;
s = exp(-j*( exp(j*( exp(j*(pi/4)) )) ));
belta = sin(pi/4)(sqrt(60));
K=3;
H = eig( randn(10
K,10*K) );
M = reshape(H, K, 10).’;
h1=M’;

cvx_begin
variable B(10,10K) complex
variable x1(10,K) complex
A =cvx(zeros(10,10));
for k=1:K
A1=B(:,(10
(k-1)+1):(10k));
A=A+A1;
end
minimize( trace_inv(A) );
subject to
for k=1:K
x=x1(:,k);
h=h1(k,:);
[A1 x;…
x’ 1]==hermitian_semidefinite(11);
real(h
xs)sin(pi/4) - abs( imag(hxs) )*cos(pi/4) >= belta;
end
cvx_end

## Calling SDPT3 4.0: 973 variables, 499 equality constraints

num. of constraints = 499
dim. of sdp var = 106, num. of sdp blk = 4
dim. of socp var = 6, num. of socp blk = 3
dim. of linear var = 4
dim. of free var = 200 *** convert ublk to lblk

SDPT3: Infeasible path-following algorithms

## number of iterations = 22 primal objective value = 9.91274189e-04 dual objective value = 1.36655253e-03 gap := trace(XZ) = 2.58e-04 relative gap = 2.57e-04 actual relative gap = -3.74e-04 rel. primal infeas (scaled problem) = 1.97e-10 rel. dual " " " = 1.57e-06 rel. primal infeas (unscaled problem) = 0.00e+00 rel. dual " " " = 0.00e+00 norm(X), norm(y), norm(Z) = 5.7e+04, 4.3e-04, 2.4e+00 norm(A), norm(b), norm© = 2.4e+01, 1.1e+01, 3.4e+00 Total CPU time (secs) = 0.70 CPU time per iteration = 0.03 termination code = -5 DIMACS: 3.4e-10 0.0e+00 2.7e-06 0.0e+00 -3.7e-04 2.6e-04

Status: Failed
Optimal value (cvx_optval): NaN

I don’t know how to solve this problem.Can you help me?Thank you!

Try sedumi. If you have access to Mosek, try that and show all solver and CVX output.