I’m attempting to solve a linear semidefinite program with the standard form

min dot(a,f)

subject to a_1*O_1+…+a_n*O_n + M >= 0

where a is a real vector being optimized, f is a constant vector. {O_j} is a set of orthonormal hermitian matrices and M is a positive definite hermitian matrix (typically the smallest eigenvalue ~ 10^-12). For my application, it is necessary that the positivity constraint is strictly satisfied. I have read the section on strict inequalities and it doesn’t appear that any of the suggested solutions are applicable. Is it possible to somehow transform this problem to enforce the constraint (the solution for a does not need to be “exact”) with CVX or some other solver?