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
N1 - Funding Information:
Acknowledgements The authors would like to thank the Associate Editor and the two anonymous referees for their useful remks, comments and suggestions that allowed to improve substantially the original version of this paper. This work was mostly carried out when the first author was a PhD student working at the Institute for Computational Science and Technology—Ho Chi Minh City, Vietnam. This research was supported by this Institute and partly, for the first author, by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) Grant 101.01-2017.315 and the Austrian Science Foundation (FWF), Grant P26640-N25.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
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
AN - SCOPUS:85030870444
VL - 70
SP - 477
EP - 495
JO - Journal of Global Optimization
JF - Journal of Global Optimization
SN - 0925-5001
IS - 2
ER -