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…
Shadow splitting methods for nonconvex optimisation: epi-approximation, convergence and saddle point avoidance
Felipe Atenas
We propose the shadow Davis-Yin three-operator splitting method to solve nonconvex optimisation problems. Its convergence analysis is based on a merit function resembling the Morea…
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…