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 × R^m → Rk and g ： R^n × R^m → R^l in each k...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 × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder 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, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.展开更多
基金Department of Mathematics,Indian Institute of Technology Patna,Patna 800 013,India
文摘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 × R^m → Rk and g ： R^n × R^m → R^l in each k-objectives as well as l-constraints. Further, appropriate duality relations are established under second-order（F, α, ρ, d）-convexity assumptions. A nontrivial example which is second-order（F, α, ρ, d）-convex but not secondorder 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, α, ρ, d）-convexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.
