Tseng's methods for inclusion problems on Hadamard manifolds. (9th December 2022)

• Record Type: Journal Article
• Authors: Khammahawong, Konrawut; Kumam, Poom; Chaipunya, Parin; Martínez-Moreno, Juan
• Is Part Of: Optimization. Volume 71:Number 15(2022)
• Page Start: 4367
• Page End: 4401
• Publication Date: 2022-12-09
• Subjects: Fixed points -- Hadamard manifolds -- inclusion problems -- maximal monotone vector fields -- monotone vector fields -- Tseng's method; 47H05 -- 47J20 -- 49J53 -- 51H25 -- 58A05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1940179
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this article, we present two Tseng's methods for finding a singularity point of an inclusion problem which is defined by means of a sum of a single-valued vector field and a multivalued vector field on a Hadamard manifold. Under standard assumptions, we prove any sequence generated by the proposed methods converges to a singularity point, whenever it exists. Moreover, applications to convex minimization problems and variational inequality problems are provided.