Skip to main content
Log in

Existence and Lagrangian duality for maximizations of set-valued functions

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

The maximization with respect to a cone of a set-valued function into possibly infinite dimensions is defined; some existence results are established; and a Lagrangian duality theory is developed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509–529, 1979.

    Google Scholar 

  2. Corley, H. W.,Duality Theory for Maximizations with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 84, pp. 560–568, 1981.

    Google Scholar 

  3. Kawasaki, H.,A Duality Theory in Multiobjective Nonlinear Programming, Mathematics of Operations Research, Vol. 7, pp. 95–110, 1982.

    Google Scholar 

  4. Klein, K., andThompson, A. C.,Theory of Correspondences, John Wiley, New York, New York, 1984.

    Google Scholar 

  5. Zangwill, W. I.,Nonlinear Programming: A Unified Approach, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.

    Google Scholar 

  6. Hogan, W. W.,Point-to-Set Maps in Mathematical Programming, SIAM Review, Vol. 15, pp. 591–603, 1973.

    Google Scholar 

  7. Robinson, S. M.,Generalized Equations and Their Solutions, Part 1: Basic Theory, Mathematical Programming Study, Vol. 10, pp. 128–141, 1979.

    Google Scholar 

  8. Clarke, F. H.,Optimization and Nonsmooth Analysis, John Wiley, New York, New York, 1983.

    Google Scholar 

  9. Corley, H. W.,An Existence Result for Maximizations with Respect to Cones, Journal of Optimization Theory and Applications, Vol. 31, pp. 277–281, 1980.

    Google Scholar 

  10. Borwein, J.,Multivalued Convexity and Optimization: A Unified Approach to Inequality and Equality Constraints, Mathematical Programming, Vol. 13, pp. 183–199, 1977.

    Google Scholar 

  11. Edwards, R.,Functional Analysis: Theory and Applications, Holt, Rinehart, and Winston, New York, New York, 1965.

    Google Scholar 

  12. Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley, New York, New York, 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by L. Cesari

Rights and permissions

Reprints and permissions

About this article

Cite this article

Corley, H.W. Existence and Lagrangian duality for maximizations of set-valued functions. J Optim Theory Appl 54, 489–501 (1987). https://doi.org/10.1007/BF00940198

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00940198

Key Words

Navigation