Why inv_pos in the restrict make this cvx-solving fail

1

When I comment other restricts out, only save ：inv_pos(E) <= P(1)* real(trace(WH(:,:,i,1)V(:,:,1)H(:,:,i,1)')) ; The cvx_status becomes ‘failed’. otherwise i save others and comment this restrict, cvx_status becomes ‘Solved’ .Here’s my code：
for s = 1:scamax
cvx_begin sdp quiet
cvx_solver sedumi
variables z_t z_r E F
variable beta_ES(N,K)
variable V(N,N,K) complex semidefinite
minimize l(1) * inv_pos(z_t) + l(2) inv_pos(z_r)
subject to
z_t * log(2) <= real(log(1+1/(E_rF_r))-(E-E_r)/(E_r(1+E_rF_r))-(F-F_r)/(F_r(1+E_r*F_r)));
z_r <= real(log(1+(P(2)real(trace(WH(:,:,i,2)V(:,:,2)H(:,:,i,2)')))/delte)/log(2));
% inv_pos(E) <= P(1) real(trace(WH(:,:,i,1)*V(:,:,1)H(:,:,i,1)')) ;
F/delte >= 1 + P(2) * real(trace(WH(:,:,i,2)*V(:,:,2)*H(:,:,i,2)')) / delte ;
real(trace(H_u(:,:,i,1)*V(:,:,1))) >= real(trace(H_u(:,:,i,2)*V(:,:,2)));
for k = 1:K
for n = 1:N
V(n,n,k) == beta_ES(n,k);
V(n,n,k) >= 0;
V(n,n,k) <= 1;
end
end
for n = 1:N
sum(beta_ES(n,:)) == 1;
end
V >= 0;
cvx_end
E_r = E;
F_r = F;
end
E_r and F_r are optimized values in iteration after cvx solving

2

Sofa. It is quite an abnormal problem.

3

Don’t use the quiet option.

Your description is not quite clear as to which result goes with which constraints being in the model. The look at the solver and CVX output.

I suspect CVX is reporting either
infeasible
unbounded
or
solver failing due to numerical problems.

If infeasible, follow all but section of the advice at Debugging infeasible models - YALMIP , which also applies to CVX.

Ir unbounded, follow the advice at Infeasible or unbounded - YALMIP , which also applies to CVX.