Optimality conditions and duality in multiobjective programming with invexity

Authors

  • Massimiliano Ferrara Department of Historical, Law, Economics and Social Sciences University Mediterranea of Reggio Calabria, Italy
  • Maria Viorica-Stefanescu Department of Mathematics, Academy of Economic Studies, Bucharest, Romania

DOI:

https://doi.org/10.2298/YJOR0802153F

Keywords:

multiobjective programming, invexity, duality

Abstract

(', ρ)-invexity has recently been introduced with the intent of generalizing invex functions in mathematical programming. Using such conditions we obtain new sufficiency results for optimality in multiobjective programming and extend some classical duality properties.

References

Caristi, G., Ferrara, M., and Stefanescu, A., “Mathematical programming with ( , ) ρ Φ −invexity”, in: Igor, V., Konnov, Dinh, The, Luc, Alexander, M., Rubinov, (eds.), Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol. 583, Springer, 2006, 167-176.

Craven, B.D., “Invex functions and constrained local minima”, Bull. Austral. Math. Soc., 24 (1981) 357-366.

Jeyakumar, Y., “Strong and weak invexity in mathematical programming”, Methods of Operations Research, 55 (1985) 109-125.

Hachimi, M., “Sufficiency and duality in differentiable multiobjective programming involving generalized type I functions”, J. Math. Anal. Appl., 296 (2004) 382-392.

Hanson, M.A., “On sufficiency of Kuhn Tucker conditions”, J. Math. Anal. Appl., 30 (1981) 545-550.

Hanson, M.A., and Mond, B., “Further generalization of convexity in mathematical programming”, J. Inform. Optim. Sci., 3 (1982) 22-35.

Liang, Z.A., Huang, H.X., and Pardalos, P.M., “Efficiency conditions and duality for a class of multiobjective fractional programming problems”, Journal of Global Optimization, 27 (2003) 447-471.

Martin, D.H., “The essence of invexity”, J. Opt. Theory. Appl., 47 (1985) 65-76.

Mishra, S.K., “Second order symmetric duality in mathematical programming with F-convexity”, European Journal of Operational Research, 127 (2000) 507-518.

Ojha, D.B., and Mukerjee, R.N., “Some results on symmetric duality of multiobjective programmes with generalized ( , ) F ρ ) invexity”, European Journal of Operational Research, 168 (2000) 333-339.

Preda, V., “On efficiency and duality for multiobjective programs”, J. Math. Anal. Appl., 166 (1992) 365-377.

Vial, J.P., “Strong and weak convexity of sets and functions”, Math. Oper. Res., 8 (1983) 231-259.

Weir, T., and Mond, B., “Generalized convexity and duality in multiple objective programming”, Bull. Austral. Math. Soc., 39 (1989) 287-299.

Zengkun, Xu, “Mixed type duality in multiobjective programming problems”, J. Math. Anal. Appl., 198 (1995) 621-635.

Yang, X.M., Yang, X.Q., and Teo, K.L., “Non-differentiable second order symmetric duality in mathematical programming with F-convexity”, European Journal of Operational Research, 144 (2003) 554-559.

Downloads

Published

2008-09-01

Issue

Vol. 18 No. 2 (2008)

Section

Research Articles

License

Copyright (c) 2008 YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.