I have an optimization problem in which the variable to optimize is, among others, a matrix $S$. However, I have the constraint that the support of $S$ (i.e., where it is non-zero) is fixed (say, $S_f$):
$S_f$ is a $N$x$N$ matrix with $1$ or $0$ in the $(i,j)$ entry if that entry has to be considered or not in the optimization problem. That is, the optimization problem has to ''fill'' the non-zero entries in an optimal way, provided the support in which the matrix is different from $0$. However this constraint (should) make the optimization problem not convex, due to the support term. How can I figure the motivation behind the non-convexity ? (Both through intuition and a proof). And the term support, how is formally defined? I see that there exists the support of a function, but not relative to an element.