modulus of total convexity – Optimization Online

Mosco stability of proximal mappings in reflexive Banach spaces

Published: 2006/04/25

Convex Optimization bregman distance, legendre function, modulus of total convexity, mosco convergence of a sequence of functions, proximal mapping relative to a convex function, relative projection onto a convex set, uniformly convex function

In this paper we establish criteria for the stability of the proximal mapping \textrm{Prox} $_{\varphi }^{f}=(\partial \varphi +\partial f)^{-1}$ associated to the proper lower semicontinuous convex functions $\varphi $ and $f$ on a reflexive Banach space $X.$ We prove that, under certain conditions, if the convex functions $\varphi _{n}$ converge in the sense of Mosco … Read more

Reduntant axioms in the definitionof Bregman functions

Published: 2002/03/17, Updated: 2004/10/04

Dan Butnariu

Charles Byrne

Yair Censor

Constrained Nonlinear Optimization bregman distance, bregman function, kullback-leibler distance, modulus of total convexity, sequential consistency, totally convex function

The definition of a Bregman function, given by Censor and Lent in 1981 on the basis of Bregman’s seminal 1967 paper, was subsequently used in a plethora of research works as a tool for building sequential and inherently parallel feasibility and optimization algorithms. Solodov and Svaiter have recently shown that it is not CitationJournal of … Read more