On general implicit hybrid iteration method for triple hierarchical variational inequalities with hierarchical variational inequality constraints. (1st September 2020)

• Record Type: Journal Article
• Authors: Ceng, Lu-Chuan; Köbis, Elisabeth; Zhao, Xiaopeng
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 1961
• Page End: 1986
• Publication Date: 2020-09-01
• Subjects: General implicit hybrid iterative algorithm -- triple hierarchical variational inequality -- Mann's implicit iteration method -- Korpelevich's extragradient method -- nonexpansive mapping; 49J30 -- 47H09 -- 47J20 -- 49M05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1703978
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we study the triple hierarchical variational inequality problem (THVIP, for short) with the hierarchical variational inequality constraint for finitely many nonexpansive mappings and an asymptotically nonexpansive mapping in a real Hilbert space. Based on Korpelevich's extragradient method, hybrid steepest-descent method, Mann's implicit iteration method and Halpern's iteration method, a general implicit hybrid iterative algorithm for solving this THVIP is proposed. Under mild conditions, the strong convergence of the iterative sequences generated by the algorithm is established. Our results improve and extend the corresponding results in the earlier and recent literature.