Skip to main content
SpringerLink
Log in

Verallgemeinerte Differenzierbarkeitsbegriffe und ihre Anwendung in der Optimierungstheorie

Generalized differentiability and its application in optimization theory

  • Published:
Computing Aims and scope Submit manuscript

Zusammenfassung

Es werden Differenzierbarkeitsbegriffe eingeführt, die sich zum Studium einer großen Klasse von Optimierungsaufgaben eignen. Besondere Berücksichtigung finden dabei Aufgaben mit nichtglatten Zielfunktionen und Nebenbedingungen.

Abstract

Several kinds of differentiability are defined, which are adapted to the study of a large class of optimization problems. A theory is constructed with special respect to problems with nonsmooth target-functions and side conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literatur

  1. Abadie, J.: On the Kuhn-Tucker Theorem. Nonlinear Programming, S. 21–36. Amsterdam: North-Holland Publ. Comp. 1967.

    Google Scholar 

  2. Bouligand, G.: Introduction à la Géométrie Infinitésimale directe. Paris: 1932.

  3. Danskin, J. M.: The theory of max-min and its application to weapons allocations problems. New York: Springer. 1967.

    Google Scholar 

  4. Dejanov, V. F., und A. M. Rubinov: Approximationsverfahren für Extremalaufgaben. Leningrad: Universitätsverlag. 1968 (russisch).

    Google Scholar 

  5. Dubovichii, A. Ya., and A. A. Milyutin: Extremum problems with constraints. Soviet. Math. Dokl.4, 452–455 (1963).

    Google Scholar 

  6. Dubovichii, A. Ya., and A. A. Milyutin: Extremum problems in the presence of restrictions. Z. Vycisl. Math. i Mat. Fiz.5, 395–453 (1965).

    Google Scholar 

  7. Hoffmann, K.-H.: Nichtlineare Optimierung. Habilitationsschrift, München, 1971.

  8. Kolumbán, I.: Sur un problème d'approximation optimale. Mathematica (Cluj)8, 267–273 (1966).

    Google Scholar 

  9. Krabs, W.: Nonlinear Optimization and Approximation. Erscheint in J. of Approx. Theory (1971).

  10. Laurent, P.-J.: Approximation et optimisation. Paris: Hermann. 1972.

    Google Scholar 

  11. Ljusternik, L. A., und W. J. Sobolev: Elemente der Funktionalanalysis. Berlin: Akademie-Verlag. 1968.

    Google Scholar 

  12. Mainardus, G., und D. Schwedt: Nicht-lineare Approximation. Arch. Rat. Mech.17, 297–326 (1964).

    Google Scholar 

  13. Pshenichnyi, B. N.: Necessary Conditions for an Extremum. Moscow: Nauka. 1969. (Englische Übersetzung 1971).

    Google Scholar 

  14. Rockafellar, R. T.: An extension of Fenchel's duality theorem for convex functions. Duke Math. J.33, 81–90 (1966).

    Article  Google Scholar 

  15. Russel, D. L.: The Kuhn-Tucker Conditions in Banach Space with an Application to Control Theory. J. Math. Anal. Appl.15, 200–212 (1966).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität München, Theresienstraße 39, D-8000, München 2, Bundesrepublik Deutschland

    K. -H. Hoffmann

  2. Facultatea de Matematica, Universitatea Babes-Bolyai, Str. Kogalniceanu 1, Cluj, Roumania

    I. Kolumbán

Authors
  1. K. -H. Hoffmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Kolumbán
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Mit 1 Abbildung

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hoffmann, K.H., Kolumbán, I. Verallgemeinerte Differenzierbarkeitsbegriffe und ihre Anwendung in der Optimierungstheorie. Computing 12, 17–41 (1974). https://doi.org/10.1007/BF02239497

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02239497

Search

Navigation