bregman projection – Optimization Online

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

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

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

Joint minimization with alternating Bregman proximity operators

Published: 2004/12/28

Heinz Bauschke

Patrick L. Combettes

Dominikus Noll

Convex Optimization alternating direction method, alternating projection methods, bregman distance, bregman projection, left proximity operator, moreau envelope, prox operator, proximal point algorithm, right proximity operator

A systematic study of the proximity properties of Bregman distances is carried out. This investigation leads to the introduction of a new type of proximity operator which complements the usual Bregman proximity operator. We establish key properties of these operators and utilize them to devise a new alternating procedure for solving a broad class of … Read more