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Fuzzy Γ-Operators and Convolutive Approximations

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Nonsmooth Optimization and Related Topics

Part of the book series: Ettore Majorana International Science Series ((EMISS,volume 43))

Abstract

By Γ-functional we intend the functionals built from consecutive extremizations. The simpler Γ-functionals are lower and upper limits along families of subsets:

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References

  1. H. Attouch, R. Wets. “A convergence theory for saddle functions”. Trans. Amer. Math. Soc., 280 (1983), pp. 1–41.

    Article  MathSciNet  MATH  Google Scholar 

  2. E.J. Balder. “An extension of duality-stability relations to nonconvex optimization problems”. SIAM J. Control Optim., 15 (1977), 329–343.

    Article  MathSciNet  MATH  Google Scholar 

  3. L. Cesari. “Seminormality and upper semicontinuity in optimal control”. J. Opt. Th. Appl., 6 (1970), 114–137.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. Choquet. “Sur les notions de filtre et de grille”. C.R. Ac. Sci. Paris, 224 (1947), 171–173.

    MathSciNet  MATH  Google Scholar 

  5. E. De Giorgi. “Generalized limits in calculus of variations”. In “Topics in Functional Analysis”, Quaderno Scuola Normale Superiore, Pisa (1980–81).

    Google Scholar 

  6. E. De Giorgi and T. Franzoni.“ Su un tipo di convergenza variazionale”. Atti Accademia dei Lincei, Fis. Mat. Natur, (8) 58 (1975), 842–850.

    MATH  Google Scholar 

  7. S. Dolecki. “On inf-convolutions, generalized convexity and seminormality”. Publ. Math. Limoges (1986).

    Google Scholar 

  8. S. Dolecki, G.H. Greco. “Cyrtologies of convergences I”. Math. Nachr., 126 (1986), pp. 327–348.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Dolecki, J. Guillerme, M.B. Lignola, C. Malivert. “F-inequalities and stability of generalized extremal convolutions”. To appear.

    Google Scholar 

  10. S. Dolecki and S. Kurcyusz. “On 4-convexity in extremal problems”. S1.1iJ J. Control Optim., 16 (1978), 277–300.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Fougères, A. Truffert. “Régularisation-s.c.i. et I’-convergence: approximations inf-convolutives associées à un référentiel”. Publ. AVAMAC, Univ. Perpignan, 84–08/15, Annali Mat. Pura Appl., to apper (1984).

    Google Scholar 

  12. G.S. Goodman. “The duality of convex functions and Cesari’s property Q. In ”Mathematical Control Theory“, S. Dolecki, C. Olech and J. Zabczyk (eds.), Banach Center Pubblications, I, Polish Scientific Publishers, Warszawa (1976).

    Google Scholar 

  13. G.H. Greco. “Limitoidi e reticoli completi”. Ann. Univ. Ferrara, Sez. VII, Sc. Mat.., 29 (1983), 153–164.

    MathSciNet  MATH  Google Scholar 

  14. G.H. Greco. “Teoria dos semifiltros”. 22° Sem. Bras. d’Analise, Rio de Janeiro (1985), 1–117.

    Google Scholar 

  15. J.L. Joly. “Une famille de topologies sur l’ensemble des fonctions convexes pour lesquelles la polarité est bicontinue”. J. Math. pures Appl.,52 (1973), 421–441:

    Google Scholar 

  16. P.O. Lindberg. “A generalization of Fenchel conjugation giving generalized Lagrangians and symmetric non convex duality”. In “Survey of Math. Progr. 1”, Proc. IX Intern. Math. Progr. Symp., Prékopa (ed.) North-Holland, Amsterdam (1979).

    Google Scholar 

  17. J.J. Moreau. “Inf-convolution des fonctions numériques sur un espace vectoriel”. C.R. Ac. Sci. Paris, 256 (1963), 5047–5049.

    MathSciNet  MATH  Google Scholar 

  18. J.J. Moreau. “Fonctionnelles convexes”. Sém. Equ. dérivées partielles, Collège de France, Paris, n.2 (1966–67).

    Google Scholar 

  19. M. Volle. “Conjugation par tranches”. Annali Mat. para Appl., 139 (1985), 279–311.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Univ. of Limoges, Limoges, France

    S. Dolecki

Authors
  1. S. Dolecki
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Editor information

Editors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, C.P. 6128, Succ.A, H3C 3J7, Montréal, Quebec, Canada

    F. H. Clarke

  2. Department of Applied Mathematics, Leningrad State University, Staryi Peterhof, 198904, Leningrad, USSR

    V. F. Dem’yanov

  3. Dipartimento di Mathematica, Universitá di Pisa, Via F. Buonarroti 2, 56100, Pisa, Italy

    F. Giannessi

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© 1989 Springer Science+Business Media New York

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Dolecki, S. (1989). Fuzzy Γ-Operators and Convolutive Approximations. In: Clarke, F.H., Dem’yanov, V.F., Giannessi, F. (eds) Nonsmooth Optimization and Related Topics. Ettore Majorana International Science Series, vol 43. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6019-4_8

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  • DOI: https://doi.org/10.1007/978-1-4757-6019-4_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-6021-7

  • Online ISBN: 978-1-4757-6019-4

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