Moreau-type characterizations of polar cones

被引：2

作者：

Soltan, Valeriu ^{[1
]}

机构：

[1] George Mason Univ, Dept Math Sci, 4400 Univ Dr, Fairfax, VA 22030 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 567卷

关键词：

Moreau; Cone; Decomposition; Orthogonal; Polar; Projection;

D O I：

10.1016/j.laa.2019.01.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A theorem of Moreau (1962) states that given a closed convex cone C and its (negative) polar cone C degrees in a real Hilbert space H, vectors y is an element of C and z is an element of C degrees are metric projections of a vector u is an element of H on C and C degrees, respectively, if and only if they satisfy the following conditions: y and z are orthogonal and u = y+z. We show that these conditions provide characteristic properties of polar cones C and C degrees in the family of pairs of convex subsets of H or R-n. A related result on separation of C and a convex subcone of C degrees is proved. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：45 / 62

页数：18

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