A splitting algorithm for a class of bilevel equilibrium problems involving nonexpansive mappings. (2nd October 2016)

• Record Type: Journal Article
• Authors: Duc, Phung M.; Muu, Le D.
• Is Part Of: Optimization. Volume 65:Number 10(2016)
• Page Start: 1855
• Page End: 1866
• Publication Date: 2016-10-02
• Subjects: Bilevel Equilibria -- splitting -- parallel algorithm -- nonexpansive mapping -- equilibrium constraint -- maximal monotone inclusion; 65 K10 -- 90 C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1195831
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We propose splitting, parallel algorithms for solving strongly equilibrium problems over the intersection of a finite number of closed convex sets given as the fixed-point sets of nonexpansive mappings in real Hilbert spaces. The algorithm is a combination between the gradient method and the Mann-Krasnosel'skii iterative scheme, where the projection can be computed onto each set separately rather than onto their intersection. Strong convergence is proved. Some special cases involving bilevel equilibrium problems with inverse strongly monotone variational inequality, monotone equilibrium constraints and maximal monotone inclusions are discussed. An illustrative example involving a system of integral equations is presented.