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.
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页码：1637 / 1651
页数：15
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