Generalized invexity and duality in multiobjective nonlinear programming

  • Laxminarayan Das
  • Sudarsan Nanda
Article

Abstract

The purpose of this paper is to study the duality theorems in cone constrained multiobjective nonlinear programming for pseudo-invex objectives and quasi-invex constrains and the constraint cones are arbitrary closed convex ones and not necessarily the nonnegative orthants.

AMS Mathematics Subject Classification

90C 

Key words and phrases

Multiobjective programming Mond-Weir dual generalized invex proper efficiency 

References

  1. 1.
    C.R., Bector, S. Chandra and Durga Prasad,Duality in pseudo linear multiobjective programming, Asia Pacific Journal of Operational Research 5 (1988) 150–159.MATHMathSciNetGoogle Scholar
  2. 2.
    A. Ben-Israel, and B. Mond,What is invexity? J. Aust. Math. Soc. Ser. B. 28 (1986) 1–9.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    G. Bitran,Duality in nonlinear multiple criteria optimization problems, Journ. of Optimization Theory and Applications 35(3) (1981) 367–401.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    B.D. Craven,Invex functions and constrained local minima, Bull Austral Math. Soc. 24 (1981) 357–366.MATHMathSciNetGoogle Scholar
  5. 5.
    R.R. Egudo,Proper efficiency and multi-objective duality in nonlinear programming, J. Inf. Opt. Science 8(2), (1987) 155–166.MATHMathSciNetGoogle Scholar
  6. 6.
    R.R. Egudo, and M.A. Hanson,Multi-objective duality with invexity, J. Math. Anal. Appl. 126 (1987) 469–477.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    A.M. Geoffrion,Proper efficiency and theory of vector maximization, J. Math. Anal. Appl. 22 (1968) 618–630.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    M.A. Hanson,On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981) 545–550.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    K. Kar and S. Nanda,Generalized convexity and symmetric duality in nonlinear programming, European J. Oper. Res. 48, 372–375.Google Scholar
  10. 10.
    R.N. Kaul and S. Kaur,Optimality criteria in nonlinear programming involving non-convex functions, J. Math. Anal. Appl. 105 (1985) 104–112.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    O.L. Mangasarian,Non-linear programming, Mc Graw Hill New York (1969).Google Scholar
  12. 12.
    B. Mond and T. Weir,Generalized concavity and duality. Generalized concavity in optimization and economics (1981) 263–279.Google Scholar
  13. 13.
    S. Nanda,Invex generalization of some duality results, Opsearch 25, 2 (1998) 105–111.MathSciNetGoogle Scholar
  14. 14.
    C. Singh and M.A. Hanson,Multiobjective fractional programming duality theory, Naval Research Logistics 38(6) (1991) 925–933.MATHMathSciNetGoogle Scholar
  15. 15.
    T.A. Weir,A note on invex functions and duality in multiple objective optimization, Opsearch 25 (1988) 98–104.MATHMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational & Applied Mathematics 2003

Authors and Affiliations

  • Laxminarayan Das
    • 1
  • Sudarsan Nanda
    • 1
  1. 1.Department of MathematicsIndian Institute of TechnologyKharagpurIndia

Personalised recommendations