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Transactions of the American Mathematical Society

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The radius of metric regularity

Authors: A. L. Dontchev, A. S. Lewis and R. T. Rockafellar
Journal: Trans. Amer. Math. Soc. 355 (2003), 493-517
MSC (2000): Primary 49J53; Secondary 49J52, 90C31
Published electronically: October 4, 2002
MathSciNet review: 1932710
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Abstract: Metric regularity is a central concept in variational analysis for the study of solution mappings associated with ``generalized equations'', including variational inequalities and parameterized constraint systems. Here it is employed to characterize the distance to irregularity or infeasibility with respect to perturbations of the system structure. Generalizations of the Eckart-Young theorem in numerical analysis are obtained in particular.

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Additional Information

A. L. Dontchev
Affiliation: Mathematical Reviews, American Mathematical Society, Ann Arbor, Michigan 48107-8604

A. S. Lewis
Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6

R. T. Rockafellar
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195

Keywords: Metric regularity, perturbations, distance to irregularity, distance to infeasibility, Eckart-Young theorem, Lusternik-Graves theorem, Robinson-Ursescu theorem, coderivatives
Received by editor(s): July 27, 2000
Published electronically: October 4, 2002
Additional Notes: Research partially supported by the NSF Grant DMS–9803098 for the first and the third author, and by the Natural Sciences and Engineering Research Council of Canada for the second author
Article copyright: © Copyright 2002 American Mathematical Society