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.
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.
出处
《应用数学学报》
CSCD
北大核心
2007年第4期592-603,共12页
Acta Mathematicae Applicatae Sinica
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.
