Journal
OPTIMIZATION
Volume 64, Issue 2, Pages 225-248Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/02331934.2012.745528
Keywords
90 C25; 90 C33; 65 K10; 65 K15; equilibrium problems; extragradient method; subgradient; pseudomonotonicity
Funding
- Fonds Europeens de Developpement Regional Lorraine via the FEDER project INNOMAD'
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A globally convergent algorithm for equilibrium problems with pseudomonotone bifunctions is proposed. The algorithm is based on the idea of the subgradient extragradient method for solving variational inequalities proposed by Censor et al. [Y. Censor, A. Gibali, and S. Reich, The subgradient extragradient method for solving variational inequalities in Hilbert space, J. Optim. Theory Appl. 148 (2011), 318-335.] and Armijo linesearch techniques. In addition, we give a modified version of our algorithm for finding a common point of the solution set of equilibrium problems and the fixed point set of a nonexpansive mapping. We also analyse the weak convergence of both algorithms in a real Hilbert space.
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