AI 中文总结
研究针对方向可微函数定义二阶上下近似及引入二阶穷竭器，给出其与二阶弗雷歇次微分关系、构造规则和极值条件，还探讨了在优化中的应用。
AI 中文摘要
本文针对方向可微函数定义了二阶的上下近似，引入二阶穷竭器，给出二阶弗雷歇次微分与二阶穷竭器之间的关系，给出了Lipschitz函数一阶和二阶穷竭器的构造规则以及通过穷竭器得到的充分极值条件，并讨论了穷竭器在优化中的应用。
英文摘要
The upper and lower approximations of the second order are defined for a function differentiable in the directions. Exhausters of the second order are introduced. The relation between the second-order Frechet subdifferentials and the second-order exhausters is given. A rule for constructing exhausters of the first and second orders is given for Lipschitz functions.Necessary and sufficient extremum conditions through exhausters are given. It is discussed about the use of Exhausters in optimization.
