Linear programs are desirable because the can run relatively quickly and when a solution is found we know the solution to be globally optimal. However, that is not always the case with non$-$linear programs. Under which condition can you be certain that your solution to a nonlinear program is a global optimal?

If all the non$-$linear elements are smooth with no discontinuities.

When the solution converges.

When you use a generalized reduced gradient algorithm rather than an evolutionary algorithm to solve it$.$

When the feasible space is Convex.