Skip to main content
SpringerLink
Log in

The Kuhn-Tucker relations as variationality testing conditions for unilaterally-constrained extremum problems

  • Published:
Meccanica Aims and scope Submit manuscript

Sommario

Si dimostra che a ciascun problema operazionale quadratico di minimo, a vincoli unilateri o bilateri, può associarsi una condizione di integrabilità derivabile dalla corrispondente lagrangiana.

Il test di integrabilità della soluzione ammissibile è soddisfatta se e solo se, in condizioni di continuità e differenziabilità della lagrangiana, sono soddisfatte le condizioni di Kuhn-Tucker. Se questo è il caso, il posto problema ammette formulazione variazionale rispetto alle sole soluzioni ammissibili dell'associata formulazione programmatica primale-duale.

Summary

To each unilaterally constrained quadratic extremum operational problem may be associated an integrability or variationality condition which follows from the corresponding Lagrangian functional. The variationality test for the admissible solution is satisfied if, and only if, the corresponding Kuhn-Tucker relations are met.

If such is the case, the posed problem allows for a variational formulation with respect to the only admissible solutions.

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

References

  1. Oden J. T., Reddy J. N.,Variational Methods in Theoretical Mechanics, Ed. Springer-Verlag, 1976.

  2. Duvaut G., Lions J. L.,Les inéquations en Méchanique et en Physique, Ed. Dunod, 1972.

  3. Vainberg M. M.,Variational Methods for the Study of Non Linear Operators, Ed. Holden-Day, 1964.

  4. Maier G.,A Quadratic Programming Approach for Certain Classes of Non Linear Structural Problems, Meccanica; vol. 3, n. 2, giugno 1968, pp. 121–131.

    Google Scholar 

  5. Browder F.E.,On the Unification of the Calculus of Variations and the Theory of Monotone Nonlinear Operators in Banach Spaces, Proc. Nat. Acad. Sci. USA, vol. 56, pp. 419–425.

  6. Stampacchia G.,Variational Inequalities, in «Theory and Applications of Monotone Operators», NATO Advanced Study Institute, Venice, 1968, Ed. Oderisi, 1969.

  7. Collatz L., Wetterling W.,Optimization Problems, Springer-Verlag, 1975.

Download references

Author information

Authors and Affiliations

  1. Gruppo Studi e Ricerche, SNIA, Italy

    F. Auconi

Authors
  1. F. Auconi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Auconi, F. The Kuhn-Tucker relations as variationality testing conditions for unilaterally-constrained extremum problems. Meccanica 14, 151–156 (1979). https://doi.org/10.1007/BF02128508

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02128508

Keywords

Search

Navigation