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

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.