半-r-预不变凸规划的混合对偶问题(运筹学与控制论)

半r-预不变凸函数是一类新的广义凸函数,它是r-预不变凸函数和半预不变凸函数的推广。本文对半r-预不变凸多目标规划问题的混合型对偶进行了研究。首先,给出了在可微的半r-预不变凸函数的一个性质;然后,利用半r-预不变凸函数建立了目标函数和约束函数均可微的多目标规划问题的混合型对偶,证明了目标函数和约束函数在半r-预不变凸函数条件下的弱对偶,强对偶和严格逆对偶定理;结论具有一般性,推广了涉及预不变凸函数、r-预不变凸函数和半预不变凸函数的文献的结论。

Mixed Duality for Programming with Semi-r-preinvexity Functions

In this paper,we introduced a new class of generalized convex function,called semi-r-preinvex function,which generalized r-preinvex function and semi-preinvex function.We investigated mixed type duality involving semi-r-preinvex function.Firstly,a characterization about differentiable semi-r-preinvex function is presented;secondly,we established dual model of a class of multiobjective programming involving differentiable constraint and objective function and proved the corresponded weak duality,strong duality and strictly inverse duality,which generalized the corresponded result of preinvex function,r-preinvex function and semi-preinvex function.