Generalized invexity and duality in multiobjective nonlinear programming
Article
Received:
Revised:
- 61 Downloads
- 1 Citations
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
90CKey words and phrases
Multiobjective programming Mond-Weir dual generalized invex proper efficiencyReferences
- 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.A. Ben-Israel, and B. Mond,What is invexity? J. Aust. Math. Soc. Ser. B. 28 (1986) 1–9.MATHMathSciNetCrossRefGoogle Scholar
- 3.G. Bitran,Duality in nonlinear multiple criteria optimization problems, Journ. of Optimization Theory and Applications 35(3) (1981) 367–401.MATHCrossRefMathSciNetGoogle Scholar
- 4.B.D. Craven,Invex functions and constrained local minima, Bull Austral Math. Soc. 24 (1981) 357–366.MATHMathSciNetGoogle Scholar
- 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.R.R. Egudo, and M.A. Hanson,Multi-objective duality with invexity, J. Math. Anal. Appl. 126 (1987) 469–477.MATHCrossRefMathSciNetGoogle Scholar
- 7.A.M. Geoffrion,Proper efficiency and theory of vector maximization, J. Math. Anal. Appl. 22 (1968) 618–630.MATHCrossRefMathSciNetGoogle Scholar
- 8.M.A. Hanson,On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (1981) 545–550.MATHCrossRefMathSciNetGoogle Scholar
- 9.K. Kar and S. Nanda,Generalized convexity and symmetric duality in nonlinear programming, European J. Oper. Res. 48, 372–375.Google Scholar
- 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.O.L. Mangasarian,Non-linear programming, Mc Graw Hill New York (1969).Google Scholar
- 12.B. Mond and T. Weir,Generalized concavity and duality. Generalized concavity in optimization and economics (1981) 263–279.Google Scholar
- 13.S. Nanda,Invex generalization of some duality results, Opsearch 25, 2 (1998) 105–111.MathSciNetGoogle Scholar
- 14.C. Singh and M.A. Hanson,Multiobjective fractional programming duality theory, Naval Research Logistics 38(6) (1991) 925–933.MATHMathSciNetGoogle Scholar
- 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