Hostname: page-component-89b8bd64d-ksp62 Total loading time: 0 Render date: 2026-05-09T03:00:07.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate subdifferentials and applications II

Part of: Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  26 February 2010

A. D. Ioffe
A. D. Ioffe
Affiliation:
Profsoyuznaya 85/1/202, 117279 Moscow, U.S.S.R.
Get access

Extract

We continue the study of approximate subdifferentials initiated in [3], this time for functions on arbitrary locally convex spaces. The complexity of the infinite dimensional theory is in particular determined by the fact that various approaches and definitions which are equivalent in the finite dimensional situation are, in general, no longer equivalent if the space is infinite dimensional.

MSC classification

Secondary: 46G05: Derivatives

Information

Type
Research Article
Information
Mathematika , Volume 33 , Issue 1 , June 1986 , pp. 111 - 128
Copyright
Copyright © University College London 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Aubin, J.-P. and Ekeland, I.. Applied Nonlinear Analysis (Wiley Interscience, 1984).Google Scholar
2.Clarke, F. H.. Generalized gradients and applications. Trans. Amer. Math. Soc., 205 (1975), 247–262.CrossRefGoogle Scholar
3.Iofie, A. D.. Approximate subdifferentials and applications 1. The finite dimensional theory. Trans. Amer. Math. Soc., 281 (1984), 389–416.Google Scholar
4.Ioffe, A. D.. Sous-differentielles approchees des fonctions numeriques. C.R. Acad. Sci. Paris Ser. A-B, 292 (1981), 675–678.Google Scholar
5.Iofie, A. D.. Approximate subdifferentials of nonconvex functions, Cahier #8120 (CEREMADE, Univ. Paris IX “Dauphine”, 1981).Google Scholar
6.Ioffe, A. D.. Nonsmooth analysis: differential calculus of nondifferentiable mappings. Trans. Amer. Math. Soc., 266 (1981), 1–56.CrossRefGoogle Scholar
7.Ioffe, A. D.. Calculus of Dini subdifferentials of functions and contingent coderivatives of set-values maps. Nonlinear Anal. Theory, Methods Appl., 8 (1984), 517–539.CrossRefGoogle Scholar
8.Ioffe, A. D.. On subdifferentiability spaces. Ann. N.Y. Acad. Sci., 410 (1983), 107–120.CrossRefGoogle Scholar
9.Ioffe, A. D.. Approximate subdifferentials and applications 3. To appear.Google Scholar
10.Kruger, A. Ya. and Mordukhovich, B. Sh.. Extreme points and Euler equations in nondifferentiable optimziation problems. Dokl. Akad. Nauk BSSR, 24 (1980), 684–687.Google Scholar
11.Mordukhovich, B. Sh.. Nonsmooth analysis with nonconvex generalized differentials and dual maps. Dokl. Akad. Nauk BSSR, 28 (1984), 976–979.Google Scholar
12.Rockafellar, R. T.. Proximal subgradients, marginal values and augmented Lagrangians in nonconvex optimizations. Mat. Operation Research, 6 (1981), 427–437.Google Scholar
13.Rockafellar, R. T.. Directionally Lipschitzian functions and subdifferential calculus. Proc London Math. Soc., 39 (1979), 331–355.CrossRefGoogle Scholar
14.Rockafellar, R. T.. Extension of subgradient calculus with application to optimization. To appear.Google Scholar
15.Treiman, J. S.. Clarke's gradients and epsilon-subgradients in Banach spaces. To appear.Google Scholar