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The Proximal Subgradient and Constancy

Published online by Cambridge University Press:  20 November 2018

F. H. Clarke  and
R. M. Redheffer
F. H. Clarke
Affiliation:
Centre de recherches mathématiques Université de Montréal CP6128-A Montréal, Québec H3C 3J7
R. M. Redheffer
Affiliation:
Department of Mathematics University of California Los Angeles, California 90024 U.S.A.
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Abstract

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If f is a lower semicontinuous function mapping a connected open subset of ℝn to (—∞, ∞], and if the proximal subgradient of f reduces to zero wherever it exists, then f is constant.

Résumé

Résumé

Soit f une fonction semicontinue inférieurement de U à (—∞, ∞], où U est un ensemble ouvert et connexe de ℝn. Si tout sousgradient proximal de f est nul, alors f est constante.

Keywords

28A15Nonsmooth analysis
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 30 - 32
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Clarke, F. H., Methods of Dynamic and Nonsmooth Optimization, CBMS-NSF Regional Conf. Series in Applied Mathematics 57, Society for Industrial and Applied Mathematics, Philadelphia, 1989.Google Scholar
2. Clarke, F. H., An indirect method in the calculus of variations, Trans. Amer. Math. Soc, (in press).Google Scholar