Restricted Normal Cones and the Method of Alternating Projections: Theory

被引：36

作者：

Bauschke, Heinz H. ^{[1
]}

Luke, D. Russell ^{[2
]}

Phan, Hung M. ^{[3
]}

Wang, Xianfu ^{[1
]}

机构：

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

[2] Univ Gottingen, Inst Numer & Angew Math, D-37083 Gottingen, Germany

[3] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

来源：

SET-VALUED AND VARIATIONAL ANALYSIS | 2013年 / 21卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Constraint qualification; Convex set; Friedrichs angle; Normal cone; Nonconvex set; Projection operator; Restricted normal cone; Superregularity;

D O I：

10.1007/s11228-013-0239-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce and develop the theory of restricted normal cones which generalize the classical Mordukhovich normal cone. We thoroughly study these objects from the viewpoint of constraint qualifications and regularity. Numerous examples are provided to illustrate the theory. This work provides the theoretical underpinning for a subsequent article in which these tools are applied to obtain a convergence analysis of the method of alternating projections for nonconvex sets.

引用

页码：431 / 473

页数：43

共 20 条

[1]

[Anonymous], 1997, Contemporary Mathematics

[2]

[Anonymous], CRM P LECT NOTES

[3]

[Anonymous], 1997, Parallel Optimization: Theory, Algorithms, and Applications

[4]

Bauschke HH, 2011, CMS BOOKS MATH, P1, DOI 10.1007/978-1-4419-9467-7

[5]

Borwein Jonathan, 2005, CMS Books in Mathematics

[6]

Clarke F. H., 1998, NONSMOOTH ANAL CONTR, V178, DOI 10.1007/b97650

[7]

DEUTSCH F, 1995, NATO ADV SCI INST SE, V454, P107

[8]

Deutsch FR., 2012, Best Approximation in Inner Product Spaces

[9]

Dixmier J., 1949, Bull. Soc. Math. France, V77, P11

[10] On certain inequalities and characteristic value problems for analytic functions and for functions of two variables [J].

Friedrichs, Kurt .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1937, 41 (1-3) :321-364

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