Proximal Point Algorithm for Quasi-Convex Minimization Problems in Metric Spaces. (12th March 2018)

• Record Type: Journal Article
• Authors: Khatibzadeh, Hadi; Mohebbi, Vahid
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 4(2018)
• Page Start: 438
• Page End: 448
• Publication Date: 2018-03-12
• Subjects: Δ-convergence -- Hadamard space -- metric convergence -- minimization -- proximal point algorithm -- quasi-convex; 47J35 -- 35B40 -- 65K05 -- 52A41; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1374970
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove Δ -convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.