8 papers · 1 filter
Nonmonotone subgradient methods based on a local descent lemma
Francisco J. Aragón-Artacho, Rubén Campoy, Pedro Pérez-Aros +1
In this paper we present a nonmonotone line search subgradient algorithm tailored to upper- functions. This is a family of nonsmooth and nonconvex functions that sat…
Graph splitting methods: Fixed points and strong convergence for linear subspaces
Francisco J. Aragón-Artacho, Heinz H. Bauschke, Rubén Campoy +1
In this paper, we develop a general analysis for the fixed points of the operators defining the graph splitting methods from [SIAM J. Optim., 34 (2024), pp. 1569-1594] by Bredies,…
Forward-backward algorithms devised by graphs
Francisco J. Aragón-Artacho, Rubén Campoy, César López-Pastor
In this work, we present a methodology for devising forward-backward methods for finding zeros in the sum of a finite number of maximally monotone operators. We extend the framewor…
Strengthened Splitting Methods for Computing Resolvents
Francisco J. Aragón Artacho, Rubén Campoy, Matthew K. Tam
In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually.…
Demiclosedness principles for generalized nonexpansive mappings
Sedi Bartz, Rubén Campoy, Hung M. Phan
Demiclosedness principles are powerful tools in the study of convergence of iterative methods. For instance, a multi-operator demiclosedness principle for firmly nonexpansive mappi…
Using positive spanning sets to achieve d-stationarity with the Boosted DC Algorithm
Francisco J. Aragón Artacho, Rubén Campoy, Phan T. Vuong
The Difference of Convex functions Algorithm (DCA) is widely used for minimizing the difference of two convex functions. A recently proposed accelerated version, termed BDCA for Bo…