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

Phan Tu Vuong () and Jean Jacques Strodiot ()
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Phan Tu Vuong: Vienna University of Technology
Jean Jacques Strodiot: Institute for Computational Science and Technology - HCMC (ICST)

Journal of Global Optimization, 2018, vol. 70, issue 2, No 10, 477-495

Abstract: 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.

Keywords: Maximal monotone operator; Glowinski–Le Tallec splitting method; Equilibrium problem; Nash equilibrium; Global convergence (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-017-0575-0

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