On sums and convex combinations of projectors onto convex sets

JOURNAL OF APPROXIMATION THEORY

卷:242

Article

Bauschke, Heinz H.¹  Bui, Minh N.²  Wang, Xianfu¹ 

[1] Univ British Columbia, Math, Kelowna, BC V1V 1V7, Canada

[2] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

关键词: Convex set;    Convex cone;    Convex combination;    Projection operator;    Projector;    Sum of projectors;    Partial sum property;    Monotone operator;    Proximity operator;   

DOI  :  10.1016/j.jat.2019.02.001

来源: Elsevier

【 摘 要 】

The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds. Our results unify and extend the case of linear subspaces and Zarantonello's results for projectors onto cones. A detailed analysis in the case of convex combinations is carried out, and we also establish the partial sum property for projectors onto convex cones. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free