Duality for Bregman projections onto translated cones and affine subspaces.
type: Item
instance of: scholarly article
title: Duality for Bregman projections onto translated cones and affine subspaces.
zbMATH Open document ID: 1052.90054
DOI: 10.1016/S0021-9045(02)00040-0
author: Heinz H. Bauschke
published in: Journal of Approximation Theory
publication date: 2003-05-25T00:00:00Z
review text: The author proves differently the dual characterization of Bregman projection onto linear constraints presented by \textit{S. Della Peitra}, \textit{V. Della Pietra} and \textit{J. Lafferty} [Duality and auxiliary functions for Bregman distances, Technical Report CMU-CS-01-109, School of Computer Science, Carnegie Mellon University (2002)] using the framework of convex analysis. Assuming a standard constraint qualification, the given proof is much shorter and cleaner and reveals the strange nonconvex component as a reformulation of a convex optimization problem.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 1915641
zbMATH Keywords: Affine subspace
zbMATH Keywords: Bregman distance
zbMATH Keywords: Bregman projection
zbMATH Keywords: Convex cone
zbMATH Keywords: Convex duality
zbMATH Keywords: Legendre function
zbMATH Keywords: Orthogonal complement
reviewed by: Hans Benker
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915641