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Optimality and duality with generalized convexity

  • N. G. Rueda
  • M. A. Hanson
  • C. Singh
Contributed Papers

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.

Key Words

Generalized convexity duality fractional programming multiobjective programming minmax programming 

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References

  1. 1.
    Hanson, M. A.,On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 545–550, 1981.CrossRefGoogle Scholar
  2. 2.
    Hanson, M. A., andMond, B.,Necessary and Sufficient Conditions in Constrained Optimization, Mathematical Programming, Vol. 37, pp. 51–58, 1987.Google Scholar
  3. 3.
    Bector, C. R., andSingh, C.,B-Vex Functions, Journal of Optimization Theory and Applications, Vol. 71, pp. 237–253, 1991.CrossRefGoogle Scholar
  4. 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.Google Scholar
  5. 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.Google Scholar
  6. 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. 7.
    Singh, C.,Duality Theory in Multiobjective Differentiable Programming, Journal of Information and Optimization Sciences, Vol. 9, pp. 231–240, 1988.Google Scholar
  8. 8.
    Singh, C., andHanson, M. A.,Multiobjective Fractional Programming Duality Theory, Naval Research Logistics, Vol. 38, pp. 925–933, 1991.Google Scholar
  9. 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

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • N. G. Rueda
    • 1
  • M. A. Hanson
    • 2
  • C. Singh
    • 3
  1. 1.Department of Mathematics and Computer ScienceMerrimack CollegeNorth Andover
  2. 2.Department of StatisticsFlorida State UniversityTallahassee
  3. 3.Department of MathematicsSt. Lawrence UniversityCanton

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