关键词: 局部凸线性拓扑空间, 广义方向导数, 广义梯度, Lipschitz条件, (弱)有效解.

Abstract:

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 attains some optimality sufficient conditions.

Key words: Locally convex linear topological space, Generalized directional derivative, Generalized gradient, Lipschitzian condition,(weak)efficient solution.