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...

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Bibliographic Details
Published inFoundations of computational mathematics Vol. 15; no. 6; pp. 1637 - 1651
Main Authors Drusvyatskiy, D., Ioffe, A. D., Lewis, A. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2015
Springer
Subjects
Analysis
Applications of Mathematics
Computer Science
Convex sets
Economics
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
United States
Alternating projections
Variational analysis
49M20
Linear convergence
90C30
65K10
Transversality
Slope
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ISSN1615-3375
1615-3383
DOI10.1007/s10208-015-9279-3

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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