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Variations on the Theme of Nonsmooth Analysis: Another Subdifferential

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Nondifferentiable Optimization: Motivations and Applications

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 255))

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.

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References

  1. CLARKE F.H.: Optimization and Nonsmooth Analysis. Wiley, New-York (1983).

    Google Scholar 

  2. CORNET B.: Contribution à la théorie mathématique des mécanismes dynamiques d’allocation des ressources. Thèse Univ. Paris 9 (1981).

    Google Scholar 

  3. -25, Soviet Math. Dokl. 21 (1) (1980) 14–17.

    Google Scholar 

  4. 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.

    Google Scholar 

  5. DOLECKI S., PENOT J.P.: The Clarke’s tangent cone and limits of tangent cones. Publ. Math. Pau (1983).

    Google Scholar 

  6. 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).

    Google Scholar 

  7. LINER E.: Ensembles et fonctions étoilés; application à l’optimisation et au calcul différentiel généralisé (manuscript, Toulouse) (1981).

    Google Scholar 

  8. IOFFE A.: Approximate subdifferentials and applications I: the finite dimensional theory. Trans. Amer. Math. Soc. 281 (1) (1984) 389–416.

    Google Scholar 

  9. 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.

    Article  Google Scholar 

  10. KURATOWSKI K.: Topologie, I. Polish Scientific Publisher. P.W.N. Warzaw (1958), English translation PWN - Academic Press (1966).

    Google Scholar 

  11. 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.

    Google Scholar 

  12. MICHEL P., PENOT J.P.: A simple subdifferential calculus for locally lipschitzian functions (to appear).

    Google Scholar 

  13. PENOT J.P.: Calcul sous-différentiel et optimisation, J. Funct. Anal. 27 (2) (1978) 248–276.

    Article  Google Scholar 

  14. PENOT J.P.: On regularity conditions in mathematical programming. Math. Prog. Study 19 (1982) 167–199.

    Article  Google Scholar 

  15. PENOT J.P.: A characterization of tangential regularity Anal. Theory, Methods and Appl. 5 (6) (1981) 625–643.

    Article  Google Scholar 

  16. PENOT J.P.: Generalized higher order derivatives and higher order optimality conditions (to appear).

    Google Scholar 

  17. PENOT J.P., TERPOLILLI P.: Cônes tangents et singularités. C.R. Acad. Sci. Paris 296 (1983), 721–724.

    Google Scholar 

  18. PONTRJAGIN L.S.: Linear differential games II. Dokl. Akad. Nauk 175 (1967) 764–766.

    Google Scholar 

  19. PSENICNYJ B.N.: Leçons sur les jeux différentiels. Cahier de l’IRIA n° 4 (1971) 145–226.

    Google Scholar 

  20. ROCKAFELLAR R.T.: Directionally lipschitzian functions and subdifferential calculus. Proc. London Math. Soc. 39 (1979) 331–355.

    Google Scholar 

  21. ROCKAFELLAR R.T.: Generalized directional derivatives and subgradients of nonconvex functions. Can. J. Math. 32 (2) (1980) 257–280.

    Article  Google Scholar 

  22. 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

    Google Scholar 

  23. 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.

    Article  Google Scholar 

  24. TREIMAN J.: Generalized gradients and paths of descent,Preprint, Univ. of Alaska (1984).

    Google Scholar 

  25. WATKINS G.G.: Clarke’s tangent vectors as tangents to Lipschitz continuous curves, J. Optim. Th. Appli. (to appear).

    Google Scholar 

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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

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  • 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

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