Generalized Multiobjective Symmetric Duality under Second-Order (F, α, ρ, d)-Convexity

In this paper, we first formulate a second-order multiobjective symmetric primal-dual pair over arbitrary cones by introducing two different functions f : R-n x R-m -> R-k and g : R-n x R-m -> R-l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order (F, alpha, rho, d)-convexity assumptions. A nontrivial example which is second-order (F, alpha, rho, d)-convex but not second-order convex/F-convex is also illustrated. Moreover, a second-order minimax mixed integer dual programs is formulated and a duality theorem is established using second-order (F, alpha, rho, d)-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.