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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Vydáno v:Foundations of computational mathematics Ročník 15; číslo 6; s. 1637 - 1651
Hlavní autoři: Drusvyatskiy, D., Ioffe, A. D., Lewis, A. S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2015
Témata:
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
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Abstract 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.
AbstractList 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.
Author Lewis, A. S.
Ioffe, A. D.
Drusvyatskiy, D.
Author_xml – sequence: 1
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  surname: Drusvyatskiy
  fullname: Drusvyatskiy, D.
  organization: Department of Mathematics, University of Washington
– sequence: 2
  givenname: A. D.
  surname: Ioffe
  fullname: Ioffe, A. D.
  organization: Mathematics Department, Technion-Israel Institute of Technology
– sequence: 3
  givenname: A. S.
  surname: Lewis
  fullname: Lewis, A. S.
  email: adrian.lewis@cornell.edu
  organization: ORIE, Cornell University
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Issue 6
Keywords Alternating projections
Variational analysis
49M20
Linear convergence
90C30
65K10
Transversality
Slope
Language English
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PublicationTitle Foundations of computational mathematics
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Snippet We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard...
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SubjectTerms Applications of Mathematics
Computer Science
Economics
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematics
Mathematics and Statistics
Matrix Theory
Numerical Analysis
Title Transversality and Alternating Projections for Nonconvex Sets
URI https://link.springer.com/article/10.1007/s10208-015-9279-3
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