Transversality and Alternating Projections for Nonconvex Sets

被引：57

作者：

Drusvyatskiy, D. ^{[1
]}

Ioffe, A. D. ^{[2
]}

Lewis, A. S. ^{[3
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

[3] Cornell Univ, ORIE, Ithaca, NY 14853 USA

来源：

FOUNDATIONS OF COMPUTATIONAL MATHEMATICS | 2015年 / 15卷 / 06期

基金：

美国国家科学基金会;

关键词：

Alternating projections; Linear convergence; Variational analysis; Slope; Transversality; CONVERGENCE; REGULARITY; MANIFOLDS; SARD;

D O I：

10.1007/s10208-015-9279-3

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. When the two sets are semi-algebraic and bounded, but not necessarily transversal, we nonetheless prove subsequence convergence.

引用

页码：1637 / 1651

页数：15

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