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

• Autores: Papa Quiroz, Erik A., Huaman ˜Naupa, Jose L.
• Formato: artículo
• Fecha de Publicación: 2022
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revistas - Universidad Nacional Mayor de San Marcos
• Lenguaje: español
• OAI Identifier: oai:revistasinvestigacion.unmsm.edu.pe:article/23144
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/23144
• Nivel de acceso: acceso abierto
• Materia: Kurdyka-Lojasiewicz inequality; quasi-distances; proximal point algo-rithm; Desigualdad de Kurdyka-Lojasewicz; cuasi-distancia; algoritmo de punto proximal.

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.