Artículo
An abstract proximal point algorithm
Autor/es | Leustean, Laurentiu
Nicolae, Adriana Sipos, Andrei |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2018 |
Fecha de depósito | 2018-10-10 |
Publicado en |
|
Resumen | The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing ... The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions. The algorithm works by applying successively so-called “resolvent” mappings associated to the original object that one aims to optimize. In this paper we abstract from the corresponding resolvents employed in these problems the natural notion of jointly firmly nonexpansive families of mappings. This leads to a streamlined method of proving weak convergence of this class of algorithms in the context of complete CAT(0) spaces (and hence also in Hilbert spaces). In addition, we consider the notion of uniform firm nonexpansivity in order to similarly provide a unified presentation of a case where the algorithm converges strongly. Methods which stem from proof mining, an applied subfield of logic, yield in this situation computable and low-complexity rates of convergence. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España Romanian National Authority for Scientific Research |
Identificador del proyecto | MTM2015-65242-C2-1-P
PN-II-ID-PCE-2011-3-0383 |
Cita | Leustean, L., Nicolae, A. y Sipos, A. (2018). An abstract proximal point algorithm. Journal of Global Optimization, 1-25. |
Ficheros | Tamaño | Formato | Ver | Descripción |
---|---|---|---|---|
An abstract proximal point ... | 301.9Kb | [PDF] | Ver/ | |