Hybrid projection methods for equilibrium problems with non‐Lipschitz type bifunctions

Based on the extended extragradient‐like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifu...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 40; no. 11; pp. 4065 - 4079
Main Author: Van Hieu, Dang
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 30.07.2017
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Subjects:
65K10
68W10
Algorithms
Design analysis
Equilibrium
Equilibrium methods
equilibrium problem
extragradient method
hybrid method
linesearch method
Mathematical analysis
parallel computation
Projection
subclass 90C33
Theorems
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:Based on the extended extragradient‐like method and the linesearch technique, we propose three projection methods for finding a common solution of a finite family of equilibrium problems. The linesearch used in the proposed algorithms has allowed to reduce some conditions imposed on equilibrium bifunctions. The strongly convergent theorems are established without the Lipschitz‐type condition of bifunctions. The paper also helps in the design and analysis of practical algorithms and gives us a generalization of some previously known problems. Copyright © 2017 John Wiley & Sons, Ltd.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4286