Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup
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
Keywords:
bilevel optimization, contractive mapping, nonexpansive semigroup, equilibrium problem, strong monotonicityHow to Cite
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Copyright (c) 2018 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2018 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.