[wenc]

I was talking in terms of convex optimization. The criteria for convex optimization is convex objective, convex inequality constraints and convex feasible region, and linear (not just convex) equality constraints.

I’m aware that ipopt is a local solver.

[FreakLegion]

> all nonlinear equation systems are nonconvex

> I was talking in terms of convex optimization

I'm not sure what subtlety you're pointing to here. As far as non-convex problems, though, my point is that IPOPT isn't special in this regard. Any convex solver can be a non-convex solver if you don't care about global optimality.

[wenc]

> 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.