Skip to main content
SpringerLink
Log in

Optimality and duality with generalized convexity

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

Abstract

Hanson and Mond have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given.

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

Similar content being viewed by others

References

  1. Hanson, M. A.,On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 545–550, 1981.

    Article  Google Scholar 

  2. Hanson, M. A., andMond, B.,Necessary and Sufficient Conditions in Constrained Optimization, Mathematical Programming, Vol. 37, pp. 51–58, 1987.

    Google Scholar 

  3. Bector, C. R., andSingh, C.,B-Vex Functions, Journal of Optimization Theory and Applications, Vol. 71, pp. 237–253, 1991.

    Article  Google Scholar 

  4. Bector, C. R., Suneja, S. K., andLalitha, C. S.,Generalized B-Vex Functions and Generalized B-Vex Programming, Proceedings of the Administrative Sciences Association of Canada, pp. 42–53, 1991.

  5. Bector, C. R., Suneja, S. K., andGupta, S.,Univex Functions and Univex Nonlinear Programming, Proceedings of the Administrative Sciences Association of Canada, pp. 115–124, 1992.

  6. Hanson, M. A., andMond, B.,Further Generalizations of Convexity in Mathematical Programming, Journal of Information and Optimization Sciences, Vol. 3, pp. 25–32, 1982.

    Google Scholar 

  7. Singh, C.,Duality Theory in Multiobjective Differentiable Programming, Journal of Information and Optimization Sciences, Vol. 9, pp. 231–240, 1988.

    Google Scholar 

  8. Singh, C., andHanson, M. A.,Multiobjective Fractional Programming Duality Theory, Naval Research Logistics, Vol. 38, pp. 925–933, 1991.

    Google Scholar 

  9. Bector, M. K., Husain I., Chandra, S., andBector, C. R.,A Duality Model for a Generalized Minmax Program, Naval Research Logistics, Vol. 35, pp. 493–501, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Merrimack College, North Andover, Massachusetts

    N. G. Rueda (Assistant Professor)

  2. Department of Statistics, Florida State University, Tallahassee, Florida

    M. A. Hanson (Professor)

  3. Department of Mathematics, St. Lawrence University, Canton, New York

    C. Singh (Professor)

Authors
  1. N. G. Rueda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Hanson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. A. Tapia

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rueda, N.G., Hanson, M.A. & Singh, C. Optimality and duality with generalized convexity. J Optim Theory Appl 86, 491–500 (1995). https://doi.org/10.1007/BF02192091

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02192091

Key Words

Search

Navigation