How do I have a garante that I arrived to global optimal

[Petrichor]

I have a non g-convex function. I am using conjugate gradient. I experimented also with trust region. Both solvers give me the same results, should I conclude that I am not stuck in a local minima? What should I do to verify that I atteind a global extreme?

[Nicolas Boumal]

This observation is not enough to conclude global optimality. Unless you can verify some special structure (and you already excluded g-convexity), there is no general tool that can easily allow to guarantee global optimality.