Phan, V., & Strodiot, J. J. (2018). The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces. Journal of Global Optimization, 70(2), 477–495. https://doi.org/10.1007/s10898-017-0575-0
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Journal of Global Optimization
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ISSN:
0925-5001
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Date (published):
Feb-2018
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Number of Pages:
19
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Publisher:
SPRINGER
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Peer reviewed:
Yes
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Keywords:
Computer Science Applications; Applied Mathematics; Control and Optimization; Nash equilibrium; Management Science and Operations Research; Maximal monotone operator; Glowinski-Le Tallec splitting method; Equilibrium problem; Global convergence
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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.
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Research Areas:
Modelling and Simulation: 30% Mathematical and Algorithmic Foundations: 20% Fundamental Mathematics Research: 50%
