Transversality and Alternating Projections for Nonconvex Sets

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, bu...

Full description

Saved in:
Bibliographic Details
Published in:Foundations of computational mathematics Vol. 15; no. 6; pp. 1637 - 1651
Main Authors: Drusvyatskiy, D., Ioffe, A. D., Lewis, A. S.
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2015
Subjects:
Applications of Mathematics
Computer Science
Economics
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Alternating projections
Variational analysis
49M20
Linear convergence
90C30
65K10
Transversality
Slope
ISSN:1615-3375, 1615-3383
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-015-9279-3