Abstract
In this paper, a pair of Mond-Weir type higher order fractional symmetric dual program over cone constraints is formulated. Under higher order invexity assumptions, we prove weak, strong and strict duality theorems. Moreover, a self dual program is formulated and self duality theorem is discussed.
Similar content being viewed by others
References
Agarwal, R. P., Ahmad, I., Gupta, S. K., Kailey, N.: Generalized second-order mixed symmetric duality in nondifferentiable mathematical programming. Abst. Appl. Anal. 2011 (2011). Article ID 103597
Agarwal, R. P., Ahmad, I., Gupta, S. K.: A note on higher-order nondifferentiable symmetric duality in multiobjective programming. Appl. Math. Lett. 24, 1308–1311 (2011)
Ahmad, I.: Second order symmetric duality in nondifferentiable multiobjective programming. Inf. Sci. 173, 23–34 (2005)
Bazaraa, M. S., Goode, J. J.: On symmetric duality in nonlinear programming. Oper. Res. 21, 1–9 (1973)
Chandra, S., Craven, B. D., Mond, B.: Symmetric dual fractional programming. Z. Oper. Res. 29, 59–64 (1985)
Chandra, S., Kumar, V.: A note on pseudo-invexity and symmetric duality. Eur. J. Oper. Res. 105, 626–629 (1988)
Chen, X.: Higher-order symmetric duality in nondifferentiable multiobjective programming problems. J. Math. Anal. Appl. 290, 423–435 (2004)
Dantzig, G. B., Eisenberg, E., Cottle, R. W.: Symmetric dual nonlinear programming. Pac. J. Math. 15, 809–812 (1965)
Dorn, W. S.: A symmetric dual theorem for quadratic progarms. J. Oper. Res. Soc. Jpn. 2, 93–97 (1960)
Gulati, T. R., Ahmad, I., Second-order symmetric duality for minimax mixed integer programs. Eur. J. Oper. Res. 101, 122–129 (1997)
Gulati, T. R., Ahmad, I., Husain, I.: Second-order symmetric duality with generalized convexity. Opsearch 38, 210–222 (2001)
Gulati, T. R., Gupta, S. K., Ahmad, I.: Second order symmetric duality with cone constraints. J. Comp. Appl. Math. 220, 347–354 (2008)
Gulati, T. R., Gupta, S. K.: Higher-order symmetric duality with cone constraints. Appl. Math. Lett. 22, 776–781 (2009)
Gulati, T. R., Mehndiratta, G., Verma, K.: Symmetric duality for second-order fractional programs. Optim. Lett. 7, 1341–1352 (2013)
Kassem, M.A. El-H: Symmetric and self duality in vector optimization problem. Appl. Math. Comput. 183, 1121–1126 (2006)
Kassem, M.A. El-H: Higher-order symmetric duality in vector optimization problem involving generalized cone-invex functions. Appl. Math. Comp. 209, 405–409 (2009)
Khurana, S.: Symmetric duality in multiobjective programming involving generalized cone-invex functions, European. J. Oper. Res. 165, 592–597 (2005)
Mangasarian, O. L.: Second and higher-order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607–620 (1975)
Mond, B., Weir, T.: Generalized concavity and duality. In: Schaible, S., Ziemba, W.T. (eds.) Generalized Concavity in Optimization and Economics, pp 263–280. Academic press, New York (1981)
Stancu Minasian, I. M.: A sixth bibliography of fractional programming. Optimization 55, 405–428 (2006)
Stancu Minasian, I.M.: A seventh bibliography of fractional programming. AMO-Adv. Model. Optim. 15, 309–386 (2013)
Stancu Minasian, I. M.: Fractional programming: Theory, Methods, and Applications. Kluwer Academic, Dordrecht (1997)
Yang, X.M.: On symmetric and self duality in vector optimization problem. J. Indus. Manag. Optim. 7, 523–529 (2011)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jayswal, A., Ahmad, I. & Prasad, A.K. Higher Order Fractional Symmetric Duality Over Cone Constraints. J Math Model Algor 14, 91–101 (2015). https://doi.org/10.1007/s10852-014-9259-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10852-014-9259-7