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A note on Fréchet and approximate subdifferentials of composite functions

Published online by Cambridge University Press:  17 April 2009

A. Jourani  and
L. Thibault
A. Jourani
Affiliation:
Université de Bourgogne, Laboratoire d'Analyse NumériqueB.P. 138-21004 - Dijon Cedex, France
L. Thibault
Affiliation:
Université Montpellier II, Dept. des Sciences Mathématiques, 34095 - Montpellier Cedex 5, France
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Abstract

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The aim of this note is to present in the reflexive Banach space setting a natural and simple proof of the formula of the approximate subdifferential of a composite function.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 111 - 115
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Clarke, F.H., Optimization and nonsmooth analysis (Wiley-Interscience, New York, 1983).Google Scholar
[2]Diestel, J., Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics 485 (Springer Verlag, New York, 1975).Google Scholar
[3]Abdouni, B. El and Thibault, L., ‘Lagrange multipliers for Pareto nonsmooth programming problems in Banach spaces’, Optimization 26 (1992), 277–285.CrossRefGoogle Scholar
[4]Glover, B.M. and Craven, B.D., ‘A Fritz John optimality condition using the approximate subdifferential’, Preprint (1992).Google Scholar
[5]loffe, A.D., ‘Approximate subdifferentials and applications 3: Metric theory’, Mathematika 36 (1989), 1–38.Google Scholar
[6]Ioffe, A.D., ‘Proximal analysis and aproximate subdifferentials’, J. London Math. Soc. 41 (1990), 175–192.Google Scholar
[7]Jourani, A. and Thibault, L., ‘Approximations and metric regularity in mathematical programming in Banach space’, Math. Oper. Res. 18 (1993), 390–401.CrossRefGoogle Scholar
[8]Jourani, A. and Thibault, L., ‘The approximate subdifferentials of composite functions’, Bull. Austral. Math. Soc. 47 (1993), 443–455.CrossRefGoogle Scholar
[9]Kruger, A.Ya., ‘Properties of generalized differentials’, Siberian Math. J. 26 (1985), 54–66.Google Scholar
[10]Kruger, A.Ya. and Mordukhovich, B.S., ‘Extreme points and the Euler equations in non-differentiable optimization problems’, Dokl. Akad. Nauk. BSSR 24 (1980), 684–687.Google Scholar
[11]Mordukhovich, B.S., ‘Maximum principle in the optimal time control problem with nonsmooth constraints’, J. Appl. Math. Mech. 40 (1976), 960–969.CrossRefGoogle Scholar
[12]Thibault, L., ‘Subdifferential of compactly lipschitzian vector-valued functions’, Travaux du séminaire d'analyse convexe 8 (1978), Fascicule I. Montpellier.Google Scholar