238 Int. J. Mathematics in Operational Research, Vol. 12, No. 2, 2018 Copyright © 2018 Inderscience Enterprises Ltd. Symmetric duality for multi-objective second-order fractional programs Geeta Sachdev Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women, Delhi-110006, India Email: geeta.mehndiratta@rediffmail.com Abstract: A pair of symmetric dual second-order multi-objective fractional programming programs is formulated. Various duality results are established for this pair which further helps to study minimax mixed integer programming problems. Symmetric duality theorem is established under pseudobonvexity and multiplicative separability assumptions on the functions involved. Keywords: symmetric duality; multi-objective programming; minimax mixed integer programming; fractional programming. Reference to this paper should be made as follows: Sachdev, G. (2018) ‘Symmetric duality for multi-objective second-order fractional programs’, Int. J. Mathematics in Operational Research, Vol. 12, No. 2, pp.238–252. Biographical notes: Geeta Sachdev obtained her MSc and PhD from the Department of Mathematics, IIT Roorkee. She has published 13 papers in the field of mathematical programming. Currently, she is working as an Assistant Professor in the Department of Applied Sciences and Humanities, IGDTUW, Delhi, India. 1 Introduction The concept of symmetric duality in mathematical programming introduced by Dorn (1960), has been extensively studied by several authors, namely, Dantzig et al. (1965), Mond (1965), Mond and Weir (1981) and among others. Chandra et al. (1984) studied symmetric duality in fractional programming under differentiability assumptions which was further extended by Mond (1987) involving non-differentiable fractional programs. The multi-objective analogue of symmetric dual fractional problems has been discussed in Weir (1991) and Gulati et al. (2005). Mangasarian (1975) identified second-order dual formulation for the nonlinear program. The advantage of second-order dual programs is that it provides tighter bounds for the value of the objective function of the primal problem when approximations are used because there are more parameters involved in second-order programs. For more literature on second-order duality, one may refer to Ahmad and Husain (2013) and Gulati et al. (2008). Duality results for second-order fractional programs were first obtained by Pandey (1991) under generalised η-bonvex functions.