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 language | English |
|---|---|
| Pages (from-to) | 477–495 |
| Number of pages | 19 |
| Journal | Journal of Global Optimization |
| Volume | 70 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 9 Oct 2017 |
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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 journal › Article
TY - JOUR
T1 - The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces
AU - Vuong, Phan Tu
AU - Strodiot, Jean Jacques
PY - 2017/10/9
Y1 - 2017/10/9
N2 - 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.
AB - 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.
KW - Equilibrium problem
KW - Global convergence
KW - Glowinski–Le Tallec splitting method
KW - Maximal monotone operator
KW - Nash equilibrium
UR - http://www.mendeley.com/research/glowinskile-tallec-splitting-method-revisited-framework-equilibrium-problems-hilbert-spaces
U2 - 10.1007/s10898-017-0575-0
DO - 10.1007/s10898-017-0575-0
M3 - Article
VL - 70
SP - 477
EP - 495
JO - Journal of Global Optimization
JF - Journal of Global Optimization
SN - 0925-5001
IS - 2
ER -