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Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup

    Trinh Ngoc Hai Affiliation
    ; Le Qung Thuy Affiliation

Abstract

In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented.


First Published Online: 21 Nov 2018

Keyword : bilevel optimization, contractive mapping, nonexpansive semigroup, equilibrium problem, strong monotonicity

How to Cite
Hai, T., & Thuy, L. (2019). Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup. Mathematical Modelling and Analysis, 24(1), 43-61. https://doi.org/10.3846/mma.2019.004
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Jan 1, 2019
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