次可微函数的一阶最优性条件

First Order Optimality Conditions for Sub-differentiable Functions

讨论了具有等式与不等式约束条件的次可微优化问题的一阶最优性条件．在等式约束只有一个的情形下．给出了ＦｒｉｔｚＪｏｈｎ必要条件．并在一定凸性假设下．讨论了Ｋｕｈｎ－Ｔｕｃｋｅｒ必要条件和充分条件．

A function is called subdifferentiable, if it is directionally differentiable and directional derivative has the form (v.d ). where is nonempty convex compact set. In this paper. the following problem is considered (P) minf(x). s. t. gi(x)≤0. i= 1. …. m. h(x)=0. where f(x). gi(x). h(x) are sub -differentiable and uniformly directionals differentiable. The Fritz John necessary condition are given and the Kuhn-Tucker conditions are also discussed.