New results on the proximal point algorithm in non-positive curvature metric spaces. (3rd July 2017)

• Record Type: Journal Article
• Authors: Khatibzadeh, Hadi; Mohebbi, Vahid; Ranjbar, Sajad
• Is Part Of: Optimization. Volume 66:Number 7(2017)
• Page Start: 1191
• Page End: 1199
• Publication Date: 2017-07-03
• Subjects: Convex minimization -- proximal point algorithm -- Halpern method -- Hadamard space -- resolvent; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1326044
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The subject of this paper is the inexact proximal point algorithm of usual and Halpern type in non-positive curvature metric spaces. We study the convergence of the sequences given by the inexact proximal point algorithm with non-summable errors. We also prove the strong convergence of the Halpern proximal point algorithm to a minimum point of the convex function. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.