局部凸空间上的泛函的非光滑分析及多目标规划  

On Nonsmooth Analysis and Multiobjective Programming in A Locally Convex Linear Topological Space

作　　者：曾韧英[1] 

机构地区：[1]重庆师范学院数学系,重庆400047

出　　处：《数学物理学报（A辑）》1999年第S1期524-530,共7页Acta Mathematica Scientia

摘　　要：该文对定义于局部凸线性拓扑空间Ｘ上的泛函引入广义方向导数、广义梯度及满足Ｌｉｐｓ－ｃｈｉｔｚ条件等概念，证明了它们的几个重要性质，并举例说明这里满足Ｌｉｐｓｃｈｉｔｚ条件的概念是Ｂａ－ｎａｃｈ空间情形的严格推广．最后，作为上述结论及方法的应用，讨论定义于Ｘ的多目标数学规划，得出若干关于弱有效解的最优性条件．At first the author introduces the definitions of generalized directional derivative, generalized gradient, and satisfied Lipschitzian condition for functions defined in a locally convex linear topological space. And then, the author gives two examples to illustrate that their Lipschitzian condition is a strict generalization for the situation of Banach space. Finally the author discusses the multiobjective programming and attain some optimality sufficient conditions.

关 键 词：局部凸线性拓补空间 广义方向导数 广义梯度 LIPSCHITZ条件 (弱)有效解 

分 类 号：O221[理学—运筹学与控制论]