Advertisement

Mixed type duality for a programming problem containing support function

  • I. Husain
  • Z. Jabeen
Article

Abstract

A mixed type dual to a programming problem containing support functions in a objective as well as constraint functions is formulated and various duality results are validated under generalized convexity and invexity conditions. Several known results are deducted as special cases.

AMS Mathematics Subject Classification

Primary 90C30 Secondary 90C11 90C20 90C26 

Key words and phrases

Programming problem support function mixed type duality generalized convexity generalized invexity 

References

  1. 1.
    C. R. Bector, S. Chandra and Abha,On mixed duality in mathematical programming, J. Math. Anal. Appl.259 (2001), 346–356.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    F. H. Clarke,A new approach to Langragian multipliers, Math. Operations Res.1 (1979), 165–174.CrossRefGoogle Scholar
  3. 3.
    I. V. Girasanov,Lectures on mathematical theory of extremum problem, Springer-Verlag, New York, 1972.Google Scholar
  4. 4.
    I. Husain, Abha and Jabeen,On nonlinear programming with suport functions, L. Appl. Math and computing10 (1–2) (2002), 83–89.MATHMathSciNetGoogle Scholar
  5. 5.
    O. L. Mangasarian,Non-linear programming, McGraw-Hill, New York, (1969).Google Scholar
  6. 6.
    B. Mond and M. Scheter,A duality theorem for a homogenous fractional programming problem, J. Optimization Theory Appl.25 (1978), 249–359.CrossRefGoogle Scholar
  7. 7.
    Mond and T. Weir,Generalized concavity and duality in generalized concavity in optimization and economics, (S. Schaible and W.T. Ziemba, Editors) Academic Press, New York, 1981.Google Scholar
  8. 8.
    M. Schecter,More on sub-gradient duality, J. Math. Anal. and Appl.71 (1979), 251–262.CrossRefMathSciNetGoogle Scholar
  9. 9.
    P. Wolfe,A duality theorem for nonlinear programming problem, Quart. Appl. Math.19 (1961), 289–244.MathSciNetGoogle Scholar
  10. 10.
    Z. Xu,Mixed type duality in multiobjective programming, J. Math. Anal. Appl.198 (1996), 135–144.CrossRefGoogle Scholar
  11. 11.
    J. Zhang and B. Mond,Duality for a class of non-differentiable continous programming problems, Bull Austral. Math. Soc.55 (1997), 29–44.MATHMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2004

Authors and Affiliations

  1. 1.Department of MathematicsNational Institute of technologySrinagarIndia

Personalised recommendations