An extragradient-type method for solving nonmonotone quasi-equilibrium problems. (4th May 2018)

• Record Type: Journal Article
• Authors: Van, N. T. T.; Strodiot, J. J.; Nguyen, V. H.; Vuong, P. T.
• Is Part Of: Optimization. Volume 67:Number 5(2018)
• Page Start: 651
• Page End: 664
• Publication Date: 2018-05-04
• Subjects: Extragradient-type method -- quasi-equilibrium problem -- nonmonotone operator -- convergence; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1416610
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, a quasi-equilibrium problem with a nonmonotone bifunction is considered in a finite-dimensional space. The primary difficulty with this problem is related to the fact that one must simultaneously solve a nonmonotone equilibrium problem and calculate a fixed point of a multivalued mapping. An extragradient-type method is presented and analysed for its solution. The convergence of the method is proved under the assumption that the solution set of an associated dual equilibrium problem is nonempty. Finally, some numerical experiments are reported.