4 papers
A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Łojasiewicz condition
Felipe Atenas, Alejandro Jofré, Pedro Pérez-Aros +1
This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semico…
Splitting Methods for Nonconvex Optimisation: Convergence and Saddle Point Avoidance Through Shadow Sequences
Felipe Atenas
In nonconvex optimisation, commonly used methods are usually shown to converge to stationary points, while guarantees of convergence to local minimisers have comparatively received…
A relaxed version of Ryu's three-operator splitting method for structured nonconvex optimization
Jan Harold Alcantara, Felipe Atenas
In this work, we propose a modification of Ryu's splitting algorithm for minimizing the sum of three functions, where two of them are convex with Lipschitz continuous gradients, an…
Understanding the Douglas-Rachford splitting method through the lenses of Moreau-type envelopes
Felipe Atenas
We analyze the Douglas-Rachford splitting method for weakly convex optimization problems, by the token of the Douglas-Rachford envelope, a merit function akin to the Moreau envelop…