Higher order duality in multiobjective fractional programming problem with generalized convexity

Authors

  • Pankaj Banaras Hindu University, Mahila Maha Vidhyalaya, Varanasi, India
  • Bhuwan Chandra Joshi Banaras Hindu University, Faculty of Science, DST-Centre for Interdisciplinary Mathematical Sciences, Varanasi, India

DOI:

https://doi.org/10.2298/YJOR170121009P

Keywords:

multiobjective fractional programming, support function, duality, higher order B -(b,ρ,θ,˜ρ,˜r)-invex function

Abstract

We have introduced higher order generalized hybrid B -(b,ρ,θ,˜ρ,˜r)-invex function. Then, we have estabilished higher order weak, strong and strict converse duality theorems for a multiobjective fractional programming problem with support function in the numerator of the objective function involving higher order generalized hybrid B -(b,ρ,θ,˜ρ,˜r)-invex functions. Our results extend and unify several results from the literature.

References

Antczak, T., "On (p, r)-Invexity type nonlinear programming problems", Journal of Mathematical Analysis and Applications, 264 (2001) 382-397.

Craven, B.D., "Invex function and constrained local minima", Bulletin of the Australian Mathematical Society, 24 (1981) 357-366.

Husain, I., and Jabeen, Z., "Second order duality for fractional programming with support functions", Opsearch, 41 (2004) 121-135.

Husain, I., and Jabeen, Z., "On fractional programming containing support functions", Journal of Applied Mathematics and Computing, 18 (2005) 361-376.

Hanson, M.A., "On sufficiency of the Kuhn-Tucker conditions", Journal of Mathematical Analysis and Applications, 80(2) (1981) 545-550.

Hanson, M.A., and Mond, B., "Necessary and sufficient conditions in constrained optimization", Mathematical Programming, 37 (1987) 51-58.

Kim, D.S., and Lee, Y.J., "Non-differentiable higher order duality in multiobjective programming involving cones", Nonlinear Analysis, 71 (2009) 2474-2480.

Mangasarian, O.L., "Second and higher-order duality in nonlinear programming", Journal of Mathematical Analysis and Applications, 51 (1975) 607-620.

Mishra, S.K., and Rueda, N.G., "Higher-order generalized invexity and duality in non-differentiable mathematical programming", Journal of Mathematical Analysis and Applications, 272 (2002) 496-506.

Mishra, S.K., and Giorgi, G., Invexity and optimization, Springer Science and Business Media, 88 (2008).

Mishra, S.K., and Rueda, N.G., "Higher-order generalized invexity and duality in mathematical programming", Journal of Mathematical Analysis and Applications, 247 (2000) 173-182.

Mond, B., and Weir, T., "Generalized convexity and higher-order duality", Journal of Mathematical Sciences, 16(18) (1981) 74-94.

Mond, B., and Zhang, J., "Higher order invexity and duality in mathematical programming", Generalized Convexity, Generalized Monotonicity: Recent Results (JP Crouzeix, et al., eds.), Kluwer Academic Publishers, printed in the Netherlands, (1998) 357-372.

Preda, V., "One efficiency and duality for multiobjective programs", Journal of Mathematical Analysis and Applications, 166 (1992) 365-377.

Rockafellar, R.T., Convex Analysis, Princeton University Press, Princeton, New Jersey, (1970).

Rueda, N.G., and Hanson, M.A., "Optimality criteria in mathematical programming involving generalized invexity", Journal of Mathematical Analysis and Applications, 130 (1988) 375-385.

Schmitendorf, W.E., "Necessary conditions and sufficient conditions for static minimax problems", Journal of Mathematical Analysis and Applications, 57 (1977) 683-693.

Verma, R.U., "Generalized hybrid B (b, ρ, θ, p̃, r̃)-invexities and efficiency conditions for multiobjective fractional programming", Tbilisi Mathematical Journal, 8 (2) (2015) 159-180.

Yang, X.M., Teo, K.L., and Yang, X.Q., "Duality for a class of non-differentiable multiobjective programming problems", Journal of Mathematical Analysis and Applications, 252 (2) (2000) 999-1005.

Yang, X.M., Teo, K.L., and Yang, X.Q., "Higher-order generalized convexity and duality in non-differentiable multiobjective mathematical programming", Journal of Mathematical Analysis and Applications, 297 (2004) 48-55.

Vial, J.P., "Strong and weak convexity of sets and functions", Mathematics of Operations Research, 8 (1983) 231-259.

Zalmai, G.J., "Generalized ( )-invex functions and global semiparametric sufficient efficiency conditions for multiobjective fractional programming problems containing arbitrary norms", Journal of Global Optimization, 36 (2006) 51-85.

Zhang, J., "Higher order convexity and duality in multiobjective programming problems", In Progress in Optimization, Springer US, (1999) 101-117.

Downloads

Published

2017-05-01

Issue

Section

Research Articles