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Halpern Subgradient Method for Pseudomonotone Equilib rium Problems in Hilbert Space

Nguyen Minh Khoa|Tran Van Thang
경북대학교 자연과학대학 수학과|2022.09|Kyungpook Mathematical Journal|제62권 제3호|pp. 533-555|DOI https://doi.org/10.5666/KMJ.2022.62.3.533

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키워드

Equilibrium problemsubgradientweakly continuouspseu domonotoneHalpern subgradient method
주제분류수학

초록

In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.

Abstract

In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.

참고문헌 (36)

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관련 논문AI추천

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