文献类型：期刊文献

中文题名：(h，■)-广义切导数与最优性条件

英文题名：(h,■)-Generalized Tangent Derivatives and Optimality Conditions

作者：盛宝怀[1];李银兴[2];刘三阳[3]

机构：[1]绍兴文理学院数学系;[2]宝鸡文理学院数学系;[3]西安电子科技大学应用数学系

年份：2007

卷号：30

期号：4

起止页码：592

中文期刊名：应用数学学报

外文期刊名：Acta Mathematicae Applicatae Sinica

收录：CSTPCD、、北大核心2004、CSCD2011_2012、北大核心、CSCD

基金：国家自然科学基金(10371024号);浙江省自然科学基金(Y604003号)资助项目.

语种：中文

中文关键词：Ben-Tal代数运算;(h,ψ)-凸函数;(h,ψ)-切锥;(h,ψ)-广义梯度;最优性条件

外文关键词：Ben-Tal algebraic operation; （h，ψ）-convex function; （h，ψ）-tangent cone;（h，ψ）-generalized gradient; optimality condition

中文摘要：借助于Ben-Tal广义代数运算定义了广义(h,■)-Clarke切锥,广义(h,■)-邻接切锥和广义(h,■)-伴随切锥,由此定义了广义(h,■)-Clarke方向导数、广义(h,■)-邻接方向导数、广义(h,■)-伴随方向导数及(h,■)-广义梯度,由此给出了具有(h,■)-凸性的的实值函数最优解的判别条件.文章是Ben-Tal代数在凸分析理论中的应用,所有结果和所用方法可以应用于多目标优化的研究.

外文摘要：The concepts of generalized （h,ψ）-Claxke tangent cone,generalized （h,ψ）-adiacent tangent cone and the generalized （h,ψ）-contingent tangent cone are introduced, from which the concepts of generalized （h,ψ）-Claxke tangent derivative, （h,ψ）-adjacent tangent derivative, （h,ψ）-contingent tangent derivative for real value function are proposed with the aid of Ben-Tal generalized algebraic operation and the properties for these derivatives axe discussed, with which the concept of （h,ψ）-generalized gradient is introduced. Finally, the necessary and sufficient optimality conditions for （h,ψ） convex function optimization is described. The paper is an application of the Ben-tal Algebraic in the convex analysis theory. The rusults obtained and the way used here can be applied to multiobjective optimization theory.