The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces

Phan Tu Vuong, Jean Jacques Strodiot

Research output: Contribution to journalArticle

Abstract

In this paper, we introduce a new approach for solving equilibrium problems in Hilbert spaces. First, we transform the equilibrium problem into the problem of finding a zero of a sum of two maximal monotone operators. Then, we solve the resulting problem using the Glowinski–Le Tallec splitting method and we obtain a linear rate of convergence depending on two parameters. In particular, we enlarge significantly the range of these parameters given rise to the convergence. We prove that the sequence generated by the new method converges to a global solution of the considered equilibrium problem. Finally, numerical tests are displayed to show the efficiency of the new approach.

Original languageEnglish
Pages (from-to)477–495
Number of pages19
JournalJournal of Global Optimization
Volume70
Issue number2
DOIs
Publication statusPublished - 9 Oct 2017

Fingerprint

Splitting Method
Hilbert spaces
Equilibrium Problem
Hilbert space
Maximal Monotone Operator
Global Solution
Two Parameters
Rate of Convergence
Transform
Converge
Zero
Range of data
Framework
Equilibrium problem

Keywords

  • Equilibrium problem
  • Global convergence
  • Glowinski–Le Tallec splitting method
  • Maximal monotone operator
  • Nash equilibrium

Cite this

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The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces. / Vuong, Phan Tu; Strodiot, Jean Jacques.

In: Journal of Global Optimization, Vol. 70, No. 2, 09.10.2017, p. 477–495.

Research output: Contribution to journalArticle

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