Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings

Bui Van Dinh; Do Sang Kim

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arXiv · 1508.03907

Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings

Bui Van Dinh·Do Sang Kim

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Abstract

In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence of the iterates generated by each method is obtained under assumptions that the fixed point mapping is quasi-nonexpansive and demiclosed at $0$, and the bifunction associated with the equilibrium problem is weakly continuous. The bifunction is assumed to be satisfying a Lipschitz-type condition when the basic iteration comes from the extragradient method. It becomes unnecessary when an Armijo back tracking linesearch is incorporated in the extragradient method.

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Bui Van Dinh, Do Sang Kim. 2015-08-17. Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings. https://arxiv.org/abs/1508.03907

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