一类I型一致不变凸条件下的极大极小分式规划问题

Minimax Fractional Programming Problem under a Class of Type I Univexity

为一个极大极小分式规划问题(P)提出了一类新的广义(F,α,ρ,θ)-d-V-I型一致不变凸函数的概念,并在此广义I型一致不变凸性条件下,获得了规划(P)的一些最优性充分条件。而且,建立了规划(P)一个新的对偶模型,并在前述条件下,证明了弱对偶、强对偶和严格逆对偶定理。本文所得结果推广和改进了文献的一些相应结果。

A new class of generalized （F,a,ρ,θ）-d-V-I type univex functions is introduced for a minimax fractional programming problem （P） and some sufficient optimality conditions for the problem （P） are obtained under the assumptions of generalized type I univexity. Moreover, a new dual model of programming （P） is formulated and weak duality, strong duality and strict converse duality theorems are proved under the aforesaid assumptions. The results obtained in this paper extend and improve some corresponding results in the literature.