Resumen: En el presente artículo introducimos un algoritmo de punto proximal inexacto usando distancias proximales para resolver el problema de desigualdad variacional cuando el operador involucrado en el modelo es pseudo-monótono y cuasi-monótono. Bajo algunas hipótesis naturales probamos que la sucesión generada por el método es convergente en el caso pseudo-monótono y débilmente convergente en el caso cuasi-monótono. Este enfoque extiende los resultados de Auslender, Teboulle y Ben-Tiba [1] y Brito et al. [3].Palabras Claves: Problema de desigualdad variacional, distancia proximal, algoritmo proximal, operador cuasi-monótono, operador pseudo-monótono.Abstract: In this paper we introduce an inexact proximal point algorithm using proximal distances for solving the variational inequality problem when the operator is pseudo-monotone and quasi-monotone. Under some natural assumptions we prove that the sequence generates by the method is convergent for the pseudo-monotone case and weakly convergent for the quasi-monotone one. This approach extends the result obtained by Auslender, Teboulle and Ben-Tiba [1] and Brito et al. [3].
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.