On the variational behaviour of functions with positive steepest descent rate

On the variational behaviour of functions with positive steepest descent rate This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and sufficiency of first-order optimality conditions are discussed. Their study is performed by employing the steepest descent rate, a rather general tool, which is adequate for a metric space analysis. The positivity of the steepest descent rate is then characterized in terms of $$\Phi $$ Φ -subdifferentials. If specialized to a Banach space setting, the resulting characterizations subsume known results on the stability of error bounds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

On the variational behaviour of functions with positive steepest descent rate

Positivity , Volume 19 (4) – Jan 29, 2015
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Publisher
Springer Basel
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0324-x
Publisher site
See Article on Publisher Site

Abstract

This paper investigates some aspects of the variational behaviour of nonsmooth functions, with special emphasis on certain stability phenomena. Relationships linking such properties as sharp minimality, superstability, error bound and sufficiency of first-order optimality conditions are discussed. Their study is performed by employing the steepest descent rate, a rather general tool, which is adequate for a metric space analysis. The positivity of the steepest descent rate is then characterized in terms of $$\Phi $$ Φ -subdifferentials. If specialized to a Banach space setting, the resulting characterizations subsume known results on the stability of error bounds.

Journal

PositivitySpringer Journals

Published: Jan 29, 2015

References

  • An exact penalty approach to constrained minimization problems on metric spaces
    Zaslavski, AJ

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