Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T14:51:59.331Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Clarke Subdifferential of an Integral Functional on Lp, 1 ≤ p < ∞

Published online by Cambridge University Press:  20 November 2018

E. Giner
E. Giner*
Affiliation:
Laboratoire Approximation et Optimisation Université Paul Sabatier 118, route de Narbonne 31062 Toulouse France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given an integral functional defined on ${{L}_{p}}$, $1\le p<\infty $, under a growth condition we give an upper bound of the Clarke directional derivative and we obtain a nice inclusion between the Clarke subdifferential of the integral functional and the set of selections of the subdifferential of the integrand.

Keywords

28A2549J5246E30Integral functionalintegrandepi-derivative
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 1 , 01 March 1998 , pp. 41 - 48
Copyright
Copyright © Canadian Mathematical Society 1998

References

1. Castaing, C. and Valadier, M., Convex analysis and measurable multifunctions. Lecture Notes in Math. 580, Springer Verlag, Berlin, 1977.Google Scholar
2. Clarke, F. H., Optimization and nonsmooth analysis. Canadian Mathematical Society Series of Monographs and Advanced Texts, Wiley Intersci. Publ., Wiley, New York, 1983.Google Scholar
3. Giner, E., Études sur les fonctionnelles intégrales. The`se d’É tat, Université de Pau, 1985.Google Scholar
4. Hiriart-Urruty, J.-B., Contributions à la programmation mathématique: cas déterministe et stochastique. Thèse, Université de Clermont-Ferrand II, 1977.Google Scholar
5. Hiriart-Urruty, J.-B., Tangent cones, generalized gradients and mathematical programming in Banach spaces. Math. Oper. Res. 14 (1979), 79–97.Google Scholar
6. Rockafellar, R. T., Integral functionals, normal integrands and measurable selections. In: Nonlinear operators and the calculus of variations. Lecture Notes in Math. 543(1976), Springer Verlag, Berlin, 157–207.Google Scholar
7. Rockafellar, R. T., Generalized directional derivatives and subgradients of nonconvex functions. Canad. J. Math. 32 (1980), 257–280.Google Scholar
8. Rockafellar, R. T., Directionally Lipschitzian functions and subdifferential calculus. Proc. London Math. Soc. 39 (1979), 331–355.Google Scholar
9. Thibault, L., Propriétés des sous-différentiels de fonctions localement lipschitziennes définies sur un espace de Banach séparable. Thèse de spécialité, Montpellier, 1976.Google Scholar