Inexact Proximal Point Method Using Quasi-Distances for Optimization of KL Functions

An inexact proximal point algorithm using quasi-distances is introduced to give a solution of a minimization problem in the Euclidean space. This algorithm has been motivated by the proximal method introduced by Attouch, Bolte and Svaiter [1] but in this case we consider quasi-distance instead of th...

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Bibliographic Details
Authors: Papa Quiroz, Erik A., Huaman ˜Naupa, Jose L.
Format: article
Status:Published version
Publication Date:2022
Country:Perú
Institution:Universidad Nacional Mayor de San Marcos
Repository:Revistas - Universidad Nacional Mayor de San Marcos
Language:Spanish
OAI Identifier:oai:revistasinvestigacion.unmsm.edu.pe:article/23144
Online Access:https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/23144
Access Level:Open access
Keyword:Kurdyka-Lojasiewicz inequality
quasi-distances
proximal point algo-rithm
Desigualdad de Kurdyka-Lojasewicz
cuasi-distancia
algoritmo de punto proximal.
Description
Summary:An inexact proximal point algorithm using quasi-distances is introduced to give a solution of a minimization problem in the Euclidean space. This algorithm has been motivated by the proximal method introduced by Attouch, Bolte and Svaiter [1] but in this case we consider quasi-distance instead of the Euclidean distance, functions satisfying the Kurdyka-Lojasewicz inequality, vector errors in the critical point of the proximal subproblems. We obtain, under some additional assumptions, the global convergence of the sequence generated by the algorithm to a critical point of the problem.