I am trying to minimize the largest component of a vector ${\bf x} = (x_1, x_2, x_3, x_4)$, where $x_1 \ge x_2 \ge x_3 \ge x_4$, such that it satisfies a set of linear inequalities given by ${\bf A} {\bf x} \le {\bf b}$. Furthermore, I want that, the Shannon entropy of the vector $x$ satisfies the following:
$$ -\sum_i x_i \log_2(x_i) = q, $$
for some constant $q$. I can write the following for the first constraint:
cvx_begin sdp
variable x(4, 1)
minimize x(1)
subject to
A * x <= b
cvx_end
However, when I try to include the second constraint, like:
quantum_entr(diag(x)) == q, I get the following error message:
Invalid constraint: {concave} == {real constant}
Is there a way to mix these two types of constraints in a semidefinite program?
