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Strong Convergence of a Bregman Projection Method for the Solution of Pseudomonotone Equilibrium Problems in Banach Spaces

Olawale Kazeem Oyewole|Lateef Olakunle Jolaoso|Kazeem Olalekan Aremu
경북대학교 자연과학대학 수학과|2024.03|Kyungpook Mathematical Journal|제64권 제1호|pp. 69-94|DOI https://doi.org/10.5666/KMJ.2024.64.1.69

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참고문헌

키워드

fixed pointBanach spacestrong convergenceequilibrium problemstrongly pseudomonotonequasi-ϕ-nonexpansive mapping
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초록

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature

Abstract

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature

참고문헌 (35)

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