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


version predcorr gam expon scale_data
HKM 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

0|0.000|0.000|2.2e+01|2.3e+03|4.1e+08| 2.600890e+03 0.000000e+00| 0:0:00| chol 1 1
1|0.996|0.989|9.0e-02|2.5e+01|9.1e+05| 2.311280e+03 -5.746118e+01| 0:0:00| chol 1 1
2|1.000|0.999|8.1e-07|2.8e-01|2.2e+03| 9.712029e+01 -7.521596e+00| 0:0:00| chol 1 1
3|0.998|1.000|1.3e-07|7.5e-02|1.0e+02| 1.229269e+00 6.502292e-02| 0:0:00| chol 1 1
4|0.991|1.000|3.5e-08|2.3e-02|8.8e+00| 2.565943e-01 4.752160e-01| 0:0:00| chol 1 1
5|0.993|0.993|8.7e-09|2.4e-03|4.7e-01| 2.468972e-01 5.006630e-01| 0:0:00| chol 1 1
6|0.922|0.644|7.4e-09|1.0e-03|1.8e-01| 1.804604e-01 3.388324e-01| 0:0:00| chol 1 1
7|0.675|0.529|4.5e-09|4.8e-04|8.7e-02| 1.280825e-01 2.385229e-01| 0:0:00| chol 1 1
8|0.424|0.517|3.7e-09|2.3e-04|4.5e-02| 9.315106e-02 1.660985e-01| 0:0:00| chol 1 1
9|0.351|0.485|2.7e-09|2.6e-04|2.7e-02| 6.731944e-02 1.195244e-01| 0:0:00| chol 1 1
10|0.284|0.498|2.1e-09|1.5e-04|1.4e-02| 4.887218e-02 8.473303e-02| 0:0:00| chol 1 1
11|0.298|0.470|1.5e-09|8.0e-05|7.8e-03| 3.487092e-02 6.185744e-02| 0:0:00| chol 1 1
12|0.247|0.509|1.1e-09|4.4e-05|4.5e-03| 2.538373e-02 4.330230e-02| 0:0:00| chol 1 1
13|0.319|0.447|7.7e-10|2.6e-05|2.5e-03| 1.788182e-02 3.233573e-02| 0:0:00| chol 1 1
14|0.215|0.543|6.1e-10|1.4e-05|1.7e-03| 1.323015e-02 2.176005e-02| 0:0:00| chol 1 1
15|0.396|0.403|3.7e-10|9.5e-06|8.8e-04| 9.073930e-03 1.694305e-02| 0:0:00| chol 1 1
16|0.177|0.619|3.0e-10|4.9e-06|8.7e-04| 6.857376e-03 1.030496e-02| 0:0:01| chol 1 1
17|0.551|0.360|1.5e-10|4.9e-06|3.6e-04| 4.503474e-03 8.378169e-03| 0:0:01| chol 1 1
18|0.117|0.680|1.8e-10|2.0e-06|6.2e-04| 3.483272e-03 4.580080e-03| 0:0:01| chol 1 1
19|0.610|0.362|1.8e-10|3.5e-06|2.7e-04| 2.174989e-03 3.765719e-03| 0:0:01| chol 1 1
20|0.141|0.554|2.2e-10|1.5e-06|2.9e-04| 1.568992e-03 2.386113e-03| 0:0:01| chol 1 1
21|0.151|0.498|2.1e-10|1.7e-06|2.8e-04| 1.357805e-03 1.751339e-03| 0:0:01| chol 1 1
22|0.136|0.388|2.0e-10|1.6e-06|2.6e-04| 9.912742e-04 1.366553e-03| 0:0:01|
stop: progress is too slow
stop: progress is bad

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.