Inertial extragradient method via viscosity approximation approach for solving equilibrium problem in Hilbert space

In this paper, we propose a new viscosity type inertial extragradient method with Armijo line-search technique for approximating a common solution of equilibrium problem with pseudo-monotone bifunction and fixed points of relatively nonexpansive mapping in a real Hilbert space. Two advantages of our...

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Bibliographic Details
Published inOptimization Vol. 70; no. 2; pp. 387 - 412
Main Authors Jolaoso, L. O., Alakoya, T. O., Taiwo, A., Mewomo, O. T.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 01.02.2021
Taylor & Francis LLC
Subjects
Algorithms
Approximation
bifunction
Convergence
equilibrium problem
extragradient method
fixed point
Hilbert space
inertial algorithm
Iterative methods
numerical result
Pseudo-monotone
Viscosity
viscosity approximation
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Summary:In this paper, we propose a new viscosity type inertial extragradient method with Armijo line-search technique for approximating a common solution of equilibrium problem with pseudo-monotone bifunction and fixed points of relatively nonexpansive mapping in a real Hilbert space. Two advantages of our algorithm are that its convergence does not require the bifunction to satisfy any Lipschitz-type condition and only one strongly convex program and one projection onto the feasible set are perform at each iteration. Under some mild conditions on the control sequences, we state and prove a strong convergence theorem and also present two numerical examples to illustrate the performance of our algorithm. The results in this paper improve and generalize many recent results in this direction in the literature.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1716752