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A duality model for a generalized minmax program

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Listed:
  • Meena K. Bector
  • I. Husain
  • S. Chandra
  • C. R. Bector

Abstract

We consider a generalized minmax programming problem, and establish, under certain weaker convexity assumptions, the Fritz John sufficient optimality conditions for such a problem. A dual program is introduced and using those optimality conditions duality theorems are proved relating the dual and the primal. Duality for the generalized fractional programming problem is considered as an application of the results proved.

Suggested Citation

  • Meena K. Bector & I. Husain & S. Chandra & C. R. Bector, 1988. "A duality model for a generalized minmax program," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 493-501, October.
    • Handle: RePEc:wly:navres:v:35:y:1988:i:5:p:493-501
    DOI: 10.1002/1520-6750(198810)35:53.0.CO;2-R
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    References listed on IDEAS

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    1. R. Jagannathan, 1966. "On Some Properties of Programming Problems in Parametric form Pertaining to Fractional Programming," Management Science, INFORMS, vol. 12(7), pages 609-615, March.
    2. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    3. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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