strict saddles – Optimization Online

Escaping strict saddle points of the Moreau envelope in nonsmooth optimization

Published: 2021/06/17

Convex and Nonsmooth Optimization model-based methods, moreau envelope, proximal algorithms, strict saddles

Recent work has shown that stochastically perturbed gradient methods can efficiently escape strict saddle points of smooth functions. We extend this body of work to nonsmooth optimization, by analyzing an inexact analogue of a stochastically perturbed gradient method applied to the Moreau envelope. The main conclusion is that a variety of algorithms for nonsmooth optimization … Read more

Active strict saddles in nonsmooth optimization

Published: 2019/12/15

Damek Davis

Dmitriy Drusvyatskiy

Nonsmooth Optimization active manifolds, kurdyka-lojasiewicz inequality, proximal algorithms, strict saddles

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems. Article Download … Read more