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

Dan Butnariu; Elena Resmerita

doi:10.1155/AAA/2006/84919

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

Dan Butnariu
, Elena Resmerita

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The aim of this paper is twofold. First, several basicmathematical concepts involved in the construction and study ofBregman type iterative algorithms are presented from a unifiedanalytic perspective. Also, some gaps in the current knowledgeabout those concepts are filled in. Second, we employ existingresults on total convexity, sequential consistency, uniformconvexity and relative projections in order to define and studythe convergence of a new Bregman type iterative method of solvingoperator equations.

Original language	English
Article number	84919
Journal	Abstract and Applied Analysis
Volume	2006
DOIs	https://doi.org/10.1155/AAA/2006/84919
State	Published - 2006

ASJC Scopus subject areas

Analysis
Applied Mathematics

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

abstract = "The aim of this paper is twofold. First, several basicmathematical concepts involved in the construction and study ofBregman type iterative algorithms are presented from a unifiedanalytic perspective. Also, some gaps in the current knowledgeabout those concepts are filled in. Second, we employ existingresults on total convexity, sequential consistency, uniformconvexity and relative projections in order to define and studythe convergence of a new Bregman type iterative method of solvingoperator equations.",

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AB - The aim of this paper is twofold. First, several basicmathematical concepts involved in the construction and study ofBregman type iterative algorithms are presented from a unifiedanalytic perspective. Also, some gaps in the current knowledgeabout those concepts are filled in. Second, we employ existingresults on total convexity, sequential consistency, uniformconvexity and relative projections in order to define and studythe convergence of a new Bregman type iterative method of solvingoperator equations.

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DO - 10.1155/AAA/2006/84919

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JO - Abstract and Applied Analysis

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

Abstract

ASJC Scopus subject areas

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