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- Title
On ergodic algorithms for equilibrium problems.
- Authors
Anh, P.; Hai, T.; Tuan, P.
- Abstract
In this paper, we present a new iteration method for solving monotone equilibrium problems. This new method is based on the ergodic iteration method Ronald and Bruck in (J Math Anal Appl 61:159-164, ) and the auxiliary problem principle Noor in (J Optim Theory Appl 122:371-386, ), but it includes the usage of symmetric and positive definite matrices. The proposed algorithm is very simple. Moreover, it simplifies the assumptions necessary in order to converge to the solution. Specifically, whereas previous methods require strong monotonicity and Lipschitz-type continuous conditions, our proposed method only requires weak monotonicity conditions. Applications to the generalized variational inequality problem and some numerical results are reported.
- Subjects
ERGODIC theory; ALGORITHMS; CONTINUOUS groups; INVARIANT measures; LIPSCHITZ spaces
- Publication
Journal of Global Optimization, 2016, Vol 64, Issue 1, p179
- ISSN
0925-5001
- Publication type
Article
- DOI
10.1007/s10898-015-0330-3