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 |
Funding
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\u2014Ho 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.
| Funders | Funder number |
|---|---|
| Austrian Science Fund | P26640-N25, P 26640 |
| National Foundation for Science and Technology Development | 101.01-2017.315 |
Keywords
- Equilibrium problem
- Global convergence
- Glowinski–Le Tallec splitting method
- Maximal monotone operator
- Nash equilibrium