A proximal point method for nonsmooth convex optimization problems in Banach spaces
type: Item
instance of: scholarly article
title: A proximal point method for nonsmooth convex optimization problems in Banach spaces
zbMATH Open document ID: 0947.90091
DOI: 10.1155/S1085337597000298
published in: Abstract and Applied Analysis
publication date: 2000-11-08T00:00:00Z
full work available at URL: https://eudml.org/doc/48552
full work available at URL: issue-1-2.html
review text: Summary: The authors show the weak convergence and stability of the proximal point method when applied to the constrained convex optimization problem in uniformly convex and uniformly smooth Banach spaces. In addition, they establish a nonasymptotic estimate of convergence rate of the sequence of functional values for the unconstrained case. This estimate depends on a geometric characteristic of the dual Banach space, namely its modulus of convexity. They apply a new technique which includes Banach space geometry, estimates of duality mappings, nonstandard Lyapunov functionals and generalized projection operators in Banach spaces.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 46N10
zbMATH DE Number: 1370673
zbMATH Keywords: weak convergence
zbMATH Keywords: stability
zbMATH Keywords: proximal point method
zbMATH Keywords: constrained convex optimization
zbMATH Keywords: smooth Banach spaces
zbMATH Keywords: convergence rate
zbMATH Keywords: modulus of convexity
Wikidata QID: Q58048661
author: Yakov Alber
author: R. S. Burachik
author: Alfredo Iusem
MaRDI profile type: Publication
OpenAlex ID: W2129284024
description: scientific article; zbMATH DE number 1370673