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Inertial Halpern-type method for solving monotone variational inequality and fixed point problems in Banach spaces
Método inercial de tipo Halpern para resolver desigualdades variacionales monótonas y problemas de punto fijo en espacios de Banach
DOI:
https://doi.org/10.15446/recolma.v58n2.121038Palabras clave:
Inertial method, Halpern Tseng’s extradient subgradient method, monotone variational inequality problem, demigeneralized mapping, Strong convergence, Banach space (en)convergencia fuerte, espacio de Banach, método inercial, método de Halpern Tseng de subgradiente, problema de desigualdad variacional monótona (es)
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In this paper, we introduce inertial Tseng’s method and Halperntype algorithm for solving monotone variational inequality and fixed point problems in 2-uniformly convex and 2-uniformly smooth real Banach spaces. We establish strong convergence of our proposed method under some assumptions on parameters without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of our main result.
En este artículo aplicamos el método de Tseng y algoritmos de tipo Halpern para resolver problema de desigualdad variacional monótona y problemas de punto fijo en espacios reales de Banach 2-uniformemente convexos y 2-uniformemente suaves. Probamos la convergencia fuerte del método propuesto bajo hipótesis sobre los parámetros que no dependen de la norma del operador. Finalmente presentamos ejemplos numéricos que ilustran nuestros resultados.
Referencias
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