Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces

In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor. 59 , 301–323 2012 ) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions ar...

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Bibliographic Details
Published in:Numerical algorithms Vol. 77; no. 3; pp. 741 - 761
Main Authors: Kim, Do Sang, Van Dinh, Bui
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2018
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Data compression
Equilibrium
Hilbert space
Iterative methods
Methods
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Parallel algorithm
65K15
90C99
68W10
Multiple set split equilibrium problem
Weak and strong convergence
65K10
Extragradient method
47J25
Pseudo-monotonicity
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor. 59 , 301–323 2012 ) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0338-5