Abstract
In this paper, a pair of symmetric dual second-order fractional programming problems is formulated and appropriate duality theorems are established. These results are then used to discuss the minimax mixed integer symmetric dual fractional programs.
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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)
Antczak T.: Generalized fractional minimax programming with B-(p,r)-invexity. J. Comput. Math. Appl. 56, 1505–1525 (2008)
Arana-Jimenez M., Ruiz-Garzn G., Rufin-Lizana A., Hernndez-Jimnez B.: A characterization of pseudoinvexity for the efficiency in non-differentiable multiobjective problems, duality. Nonlinear Anal. Theor. 73, 1109–1117 (2010)
Balas E.: Minimax and duality for linear and nonlinear mixed integer programming. In: Abadie, J. (ed.) Integer and Nonlinear Programming, North-Holland, Amsterdam (1970)
Bector C.R., Chandra S.: Second order symmetric and self-dual programs. Opsearch 23, 89–95 (1986)
Chandra S., Craven B.D., Mond B.: Symmetric dual fractional programming. Zeitschrift für Oper. Res. 29, 59–64 (1985)
Chandra S., Kumar V., Husain I.: Symmetric duality for multiplicatively separable fractional mixed integer programming problem. Optimization 37, 51–57 (1996)
Chinchuluun A., Pardalos P.M.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154, 29–50 (2007)
Chinchuluun A., Yuan D., Pardalos P.M.: Optimality conditions and duality for nondifferentiable multibjective fractional programming with generalized convexity. Ann. Oper. Res. 154, 133–147 (2007)
Craven B.D.: Lagrangean conditions and quasiduality. Bull. Aust. Math. Soc. 16, 325–339 (1977)
Dantzig G.B., Eisenberg E., Cottle R.W.: Symmetric dual nonlinear programming. Pac. J. Math. 15, 809–812 (1965)
Gulati T.R., Husain I., Ahmed A.: Multiobjective symmetric duality with invexity. Bull. Aust. Math. Soc. 56, 25–36 (1997)
Gulati T.R., Husain I., Ahmed A.: Symmetric dual multiobjective fractional programs with generalized convexity. Aligarh Bull. Math. 24, 35–43 (2005)
Gulati T.R., Ahmad I.: Second order symmetric duality for nonlinear minimax mixed integer programs. Eur. J. Oper. Res. 101, 122–129 (1997)
Gupta S.K., Kailey N., Sharma M.K.: Higher-order (F, α, ρ, d)-convexity and symmetric duality in multiobjective programming. J. Comput. Math. Appl. 60, 2373–2381 (2010)
Gupta S.K., Kailey N.: Nondifferentiable multiobjective second-order symmetric duality. Optim. Lett. 5, 125–139 (2011)
Kumar V., Husain I., Chandra S.: Symmetric duality for minimax mixed integer programming. Eur. J. Oper. Res. 80, 425–430 (1995)
Mangasarian, O.L.: Second- and higher-order duality in nonlinear programming. J. Math. Anal. Appl. 51, 607–620 (1975) (Computer Science, Technical Report 159, University of Wisconsin, 1972)
Mangasarian O.L.: Nonlinear Programming. McGraw-Hill, New York (1969)
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)
Mond B., Chandra S., Durga Prasad M.V.: Symmetric dual non-differentiable fractional programming. Indian J. Manag. Syst. 3, 1–10 (1987)
Nahak C., Nanda S.: Duality for multiobjective fractional control problem with generalized invexity. Appl. Math. Comput. 5, 433–466 (1998)
Suneja S.K., Lalitha C.S., Khurana S.: Second order symmetric duality in multiobjective programming. Eur. J. Oper. Res. 144, 492–500 (2003)
Suneja S.K., Srivastava M.K., Bhatia M.: Higher order duality in multiobjective fractional programming with support functions. J. Math. Anal. Appl. 347, 8–17 (2008)
Weir T., Mond B.: Symmetric and self duality in multiple objective programming. Asia Pac. J. Oper. Res. 5, 124–133 (1988)
Weir T.: Symmetric dual multiobjective fractional programming. J. Aust. Math. Soc. Ser. A 50, 67–74 (1991)
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Gulati, T.R., Mehndiratta, G. & Verma, K. Symmetric duality for second-order fractional programs. Optim Lett 7, 1341–1352 (2013). https://doi.org/10.1007/s11590-012-0507-3
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DOI: https://doi.org/10.1007/s11590-012-0507-3