> Any convex solver can be a non-convex solver if you don't care about global optimality.

Aside: Structurally I’m not sure how this would be true.

Convex solvers have very specific forms. For instance a QP solver requires a very particular form and does not admit any arbitrary non convex form except for one: the non-PSD Hessian which is the concave problem.

My point is that all NLEs power inside an optimization problem gives rise to a non convex optimization problem with no guarantee of a global solution. So convex optimization is not applicable here.