Elena Resmerita – 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

Bregman distances, totally convex functions and a method for solving operator equations in Banach spaces

Published: 2005/01/16, Updated: 2005/01/18

Dan Butnariu

Elena Resmerita

Convex and Nonsmooth Optimization bregman distance, bregman projection, e-space, essential strict convexity, inverse monotone operator, inverse strongly-monotone operator, mosco convergence, relative projection, total convexity, uniform convexity

The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity … Read more