Abstract
Making one’s way through various kinds of limits of differential quotients in order to define generalized derivativesis a rather dull task: one has to be very careful about the moving or fixed ingredients.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
CLARKE F.H.: Optimization and Nonsmooth Analysis. Wiley, New-York (1983).
CORNET B.: Contribution à la théorie mathématique des mécanismes dynamiques d’allocation des ressources. Thèse Univ. Paris 9 (1981).
-25, Soviet Math. Dokl. 21 (1) (1980) 14–17.
DOLECKI S.: Hypertangent cones for a special class of sets. in “Optimization, theory and algorithms”, J.B. Hiriart-Urruty et al. editors, Marcel. Dekker, New-York (1983) pp. 3–11.
DOLECKI S., PENOT J.P.: The Clarke’s tangent cone and limits of tangent cones. Publ. Math. Pau (1983).
FRANKOWSKA H.: The adjoint differential inclusions associated to a minimal trajectoryof a differential inclusion. Cahiers de Math. de la Décision n° 8315, Univ. Paris I X (1983).
LINER E.: Ensembles et fonctions étoilés; application à l’optimisation et au calcul différentiel généralisé (manuscript, Toulouse) (1981).
IOFFE A.: Approximate subdifferentials and applications I: the finite dimensional theory. Trans. Amer. Math. Soc. 281 (1) (1984) 389–416.
IOFFE A.: Calculus of Dini subdifferentials of functions and contingent coderivatives of set-valued maps. Nonlinear Anal. Th. Methods and Appl. 8 (5) (1984) 517–539.
KURATOWSKI K.: Topologie, I. Polish Scientific Publisher. P.W.N. Warzaw (1958), English translation PWN - Academic Press (1966).
MICHEL P., PENOT J.P.: Calcul sous-différentiel pour des fonctions lipschitziennes et non lipschitziennes. C.R. Acad. Sc. Paris I 298 (12) (1984) 269–272.
MICHEL P., PENOT J.P.: A simple subdifferential calculus for locally lipschitzian functions (to appear).
PENOT J.P.: Calcul sous-différentiel et optimisation, J. Funct. Anal. 27 (2) (1978) 248–276.
PENOT J.P.: On regularity conditions in mathematical programming. Math. Prog. Study 19 (1982) 167–199.
PENOT J.P.: A characterization of tangential regularity Anal. Theory, Methods and Appl. 5 (6) (1981) 625–643.
PENOT J.P.: Generalized higher order derivatives and higher order optimality conditions (to appear).
PENOT J.P., TERPOLILLI P.: Cônes tangents et singularités. C.R. Acad. Sci. Paris 296 (1983), 721–724.
PONTRJAGIN L.S.: Linear differential games II. Dokl. Akad. Nauk 175 (1967) 764–766.
PSENICNYJ B.N.: Leçons sur les jeux différentiels. Cahier de l’IRIA n° 4 (1971) 145–226.
ROCKAFELLAR R.T.: Directionally lipschitzian functions and subdifferential calculus. Proc. London Math. Soc. 39 (1979) 331–355.
ROCKAFELLAR R.T.: Generalized directional derivatives and subgradients of nonconvex functions. Can. J. Math. 32 (2) (1980) 257–280.
ROCKAFELLAR R.T. Generalized subgradients. in “Mathematical Pro- gramming: the State of the Art”, Bonn 1982, A. Bachen, M. Grötschel, B. Korte, editors, Springer Verlag, Berlin (1983) 368–390
TREIMAN J.: Characterization of Clarke’s tangent and normal cones in finite and infinite dimensions. Nonlinear Anal. Th., Methods and Appl. 7 (7) (1983) 771–783.
TREIMAN J.: Generalized gradients and paths of descent,Preprint, Univ. of Alaska (1984).
WATKINS G.G.: Clarke’s tangent vectors as tangents to Lipschitz continuous curves, J. Optim. Th. Appli. (to appear).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Penot, JP. (1985). Variations on the Theme of Nonsmooth Analysis: Another Subdifferential. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-12603-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15979-7
Online ISBN: 978-3-662-12603-5
eBook Packages: Springer Book Archive