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math.OC2022★ 16 cited
The effect of smooth parametrizations on nonconvex optimization landscapes
Eitan Levin, Joe Kileel, Nicolas Boumal
We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for…
math.OC2022
Computing second-order points under equality constraints: revisiting Fletcher's augmented Lagrangian
Florentin Goyens, Armin Eftekhari, Nicolas Boumal
We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate firs…