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

Dan Butnariu (dbutnarumath.haifa.ac.il)
Elena Resmerita (elena.resmeritaoeaw.ac.at)

Abstract: 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 and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations.

Keywords: Bregman distance, Bregman projection, relative projection, total convexity, essential strict convexity, E-space, Mosco convergence, uniform convexity, inverse monotone operator, inverse strongly-monotone operator.

Category 1: Convex and Nonsmooth Optimization

Citation: submitted, 2004

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Entry Submitted: 01/16/2005
Entry Accepted: 01/17/2005
Entry Last Modified: 01/18/2005

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