A modified projection algorithm for constrained equilibrium problems. (2nd December 2017)

• Record Type: Journal Article
• Authors: Santos, P. S. M.; Scheimberg, S.
• Is Part Of: Optimization. Volume 66:Number 12(2017)
• Page Start: 2051
• Page End: 2062
• Publication Date: 2017-12-02
• Subjects: Projection method -- equilibrium problem -- constrained equilibrium problem -- split equilibrium problem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1182528
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : Based on the constrained variational inequality problem considered by Censor, Gibali and Reich (Numerical Algorithms, 2012), we propose, the constrained equilibrium problem (CEP), which consists in finding a point in the intersection of two nonempty, closed and convex subsets of an Euclidean space, C and D, such that is a solution of an equilibrium problem on C . In this work, an algorithm using projections is proposed to solve (CEP). Convergence properties of the algorithm are established under mild assumptions. Some numerical results are reported.