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

Kim, D.S. and Van Dinh, B. (2018) Parallel extragradient algorithms for multiple set split equilibrium problems in Hilbert spaces. Numerical Algorithms, 77 (3). pp. 741-761. ISSN 10171398

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Abstract

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. © 2017, Springer Science+Business Media New York.

Item Type: Article
Divisions: Faculties > Faculty of Information Technology
Identification Number: 10.1007/s11075-017-0338-5
Additional Information: Language of original document: English.
URI: http://eprints.lqdtu.edu.vn/id/eprint/9590

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