An algorithm based on the generalized D-gap function for equilibrium problems

Authors:
Liping Zhang;Soon-Yi Wu
Affiliations:
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;Department of Mathematics, National Cheng Kung University, Tainan, Taiwan and National Center for Theoretical Sciences, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

The equilibrium problem (EP) can be reformulated as an unconstrained minimization problem through the generalized D-gap function. In this paper, we propose an algorithm for minimizing the problem and analyze some convergence properties of the proposed algorithm. Under some reasonable conditions, we show that the iteration sequence generated by the algorithm is globally convergent and converges to a solution to the EP and the generalized D-gap function provides a global error bound for the algorithm.