------------------------------------------------------------ Status: Unbounded Optimal value (cvx_optval): +Inf ,can any one help on this please

1 
clear;clc;close all;
ya = 1e15; %penality f
Vt = rand(2,1);
Vt = (exp(1i*Vt)*exp(1i*Vt)');
[lambda,~] = eigs(Vt,1,'largestabs');
cvx_begin sdp
    variable V(2,2) hermitian semidefinite
   variable t
    maximize(t)
    subject to
        diag(V) == 1
        -ya * real(trace(V))- real(trace(lambda*lambda'*(V-Vt))) <= t
        t>=0
cvx_end
2

-ya * real(trace(V))- real(trace(lambda*lambda'*(V-Vt))) <= t
doesn’t stop t from being as large as it wants,. You need to reexamine what the correct mathematical formulation is for whatever you’re trying to do, which I have no idea what that is.

Note that given the constraints, trace(V) must equal 2, and eye(2) is a feasible value for V.

As a secondary matter, using a value of 1e15 is not a good idea. It will cause problems. But the unboundedness is regardless of that huge value.

3

Thank you for your replay! here is the obj.that i want to optimize

clear;clc;close all;
ya = 1e6; %penality f
p_e=0.5;
sigma_b=1;
Vt = rand(2,1);
Vt = (exp(1i*Vt)*exp(1i*Vt)');
[lambda,~] = eigs(Vt,1,'largestabs');
mu_2t=trace(Vt);
cvx_begin sdp
    variable V(2,2) hermitian semidefinite
    variable mu_2
   A_0_up =  -rel_entr(1,real(inv_pos(real(p_e * mu_2t) + sigma_b)))* (p_e * (mu_2 - mu_2t)); 
   t=A_0_up-ya * real(trace(V))- real(trace(lambda*lambda'*(V-Vt)));
    maximize(real(t))
    subject to
        diag(V) == 1
        t>=0;
     
cvx_end
4

mu_2 can be made an arbitrarily large magnitude negative number, making the objective arbitrarily large, i.e., the problem is unbounded.

it is still the case that “You need to reexamine what the correct mathematical formulation is for whatever you’re trying to do, which I have no idea what that is.”

5

thank you for your response!