Simple proximal-type algorithms for equilibrium problems

This paper proposes two simple and elegant proximal-type algorithms to solve equilibrium problems with pseudo-monotone bifunctions in the setting of Hilbert spaces. The proposed algorithms use one proximal point evaluation of the bifunction at each iteration. Consequently, prove that the sequences o...

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Bibliographic Details
Published inJournal of global optimization Vol. 89; no. 4; pp. 1069 - 1098
Main Authors Yao, Yonghong, Adamu, Abubakar, Shehu, Yekini, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2024
Springer
Springer Nature B.V
Subjects
Algorithms
Computer Science
Convergence
Design standards
Efficiency
Equilibrium
Hilbert space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
68Q25
90C30
Equilibrium problems
90C25
90C60
Proximal-type algorithm
Convergence
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Summary:This paper proposes two simple and elegant proximal-type algorithms to solve equilibrium problems with pseudo-monotone bifunctions in the setting of Hilbert spaces. The proposed algorithms use one proximal point evaluation of the bifunction at each iteration. Consequently, prove that the sequences of iterates generated by the first algorithm converge weakly to a solution of the equilibrium problem (assuming existence) and obtain a linear convergence rate under standard assumptions. We also design a viscosity version of the first algorithm and obtain its corresponding strong convergence result. Some popular existing algorithms in the literature are recovered. We finally give some numerical tests and compare our algorithms with some related ones to show the performance and efficiency of our proposed algorithms.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01377-1