I am trying to solve the following problem in CVX

cvx_begin sdp quiet

variable X(4*Nr,4*Nr) hermitian

minimize( trace(E0_TOT*X))
subject to
trace(FF1*X)>=1;

trace(FF2*X)>=1;

X>=0;

cvx_end

matrices E0_TOT, FF1 and FF2 are all positive semi-definite matrices. Where

FF1=p1*E1-E2;
FF2=p2*E3-E4;

E1 and E2 are matrices with small valued entries in the order of 1e-27 while E2 and E4 have entries in the order of 1e-14. Due to the selected values for the p1 and p2 there is no worries about the feasibility but it seems that CVX cannot solve the problem in enough steps and gives the “infeasible” message.

I tried to play with cvx_precision function but it only works when I set something like cvx_precision([0.65 0.65 0.9]) which gives a result for X which by far violates the constraints.

It would be highly appreciated if you kindly help me with this issue.

Thanks.