An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces

In this paper, we introduce an explicit subgradient extragradient algorithm for solving equilibrium problem with a bifunction satisfying pseudomonotone and Lipschitz-like condition in a 2-uniformly convex and uniformly smooth Banach space. We also defined a new self-adaptive stepsize rule and prove...

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Bibliographic Details
Published in:Numerical algorithms Vol. 89; no. 2; pp. 583 - 610
Main Authors: Jolaoso, Lateef Olakunle, Aphane, Maggie
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2022
Springer Nature B.V
Subjects:
Adaptive algorithms
Algebra
Algorithms
Banach spaces
Computer Science
Equilibrium
Hilbert space
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Regularization methods
Theory of Computation
65K15
Equilibrium problem
90C33
Extragradient method
Banach spaces
47J25
Pseudomonotone
Self adaptive stepsize
65J15
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we introduce an explicit subgradient extragradient algorithm for solving equilibrium problem with a bifunction satisfying pseudomonotone and Lipschitz-like condition in a 2-uniformly convex and uniformly smooth Banach space. We also defined a new self-adaptive stepsize rule and prove a convergence result for solving the equilibrium problem without any prior estimate of the Lipschitz-like constants of the bifunction. Furthermore, we provide some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm. This result improves and extends many recent results in this direction in the literature.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-021-01126-5