摘要
本文定义了几种(h,φ)-广义凸性及(h,φ)-广义单调性,讨论了广义(h,φ)-方向导数与Clarke方向导数,广义(h,φ)-梯度集与Clarke梯度集等的相关关系.利用此关系证明了这些广义凸性与广义单调性之间的相关关系,同时还揭示了这些广义凸性、单调性与通常广义凸性,单调性存在的内在联系.
In this paper we defined some generalized convexities and generalized monotone basing on the generalized Ben-Tal algebraic operation. Then we considered the relation between （h, φ）-generalized directional derivative and Clarke directional derivative, and discussed the relations of these convexity and monotone.
出处
《运筹学学报》
CSCD
北大核心
2008年第2期88-96,共9页
Operations Research Transactions
基金
广东省教育厅自然科学基金课题(04J012).
关键词
运筹学
Ben-Tal代数运算
(h
φ)-广义凸
(h
φ)-广义单调
广义(h
φ)-方向导数
Clarke方向导数
广义(h
φ)-梯度
Operations research, generalized Ben-Tal algebraic, convex function, （h, φ）-generalized convexity, （h, φ）-generalized Monotone, （h, φ）-generalized directional derivative, Clarke directional derivative, （h, φ）-gradient.
