Second order symmetric duality for nonlinear multiobjective mixed integer programming

9 Abstract 10 We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for 11 arbitrary cones. By using the concept of efficiency and second order invexity, we establish the weak, strong, converse 12 and self-duality theorems for our dual models. Several known results are obtained as special cases. 17 Following the earlier works of Dorn [5], Dantzig et al. [3] and Mond [13] on symmetric duality, many 18 researchers attempted to generalize the formulation and weaken the convexity–concavity hypothesis re-19 quired on the kernel function f ðx; yÞ. Mond and Weir [13] weakened the convexity-concavity hypothesis for 20 f ðx; yÞ to pseudo-convexity–pseudo-concavity. Balas [1] examined the symmetric duality results of Dantzig 21 et al. [3] when some primal and dual variables are constrained to belong to some arbitrary set, for example, 22 the set of integers. 23 Nanda and Das [14] formulated a pair of symmetric dual nonlinear programming problems for arbitrary 24 cones. Kim et al. [7] proved multiobjective symmetric dual programs for arbitrary cones. Devi [4] for-25 mulated a pair of second order symmetric dual programs and established duality results involving second 26 order invex functions. Mishra [10] formulated a pair of multiobjective second order symmetric dual non-27 linear problems under second order pseudo-invexity assumptions on the functions involved and arbitrary q