Iterative methods for solving monotone equilibrium problems via dual gap functions
This paper proposes an iterative method for solving strongly monotone equilibrium problems by using gap functions combined with double projection-type mappings. Global convergence of the proposed algorithm is proved and its complexity is estimated. This algorithm is then coupled with the proximal point method to generate a new algorithm for solving monotone equilibrium problems. A class of linear equilibrium problems is investigated and numerical examples are implemented to verify our algorithms.
KeywordsGap function Double projection-type method Monotone equilibrium problem Proximal point method Global convergence Complexity
Unable to display preview. Download preview PDF.
- 6.Konnov, I.V.: Generalized convexity and related topics. In: Konnov, I.V., Luc, D.T., Rubinov, A.M. (eds.) Combined Relaxation Methods for Generalized Monotone Variational Inequalities, pp. 3–31. Springer, Berlin (2007) Google Scholar
- 15.Nesterov, Y., Scrimali, L.: Solving strongly monotone variational and quasi-variational inequalities. CORE discussion paper #107, pp. 1–15 (2006) Google Scholar
- 16.Nguyen, V.H.: Lecture notes on equilibrium problems. CIUF-CUD Summer School on Optimization and Applied Mathematics, Nha Trang, Vietnam (2002) Google Scholar