关于非光滑函数凸性的研究

Research on Convexity of Nonsmooth Functions

目的 解决多元函数的方向导数问题.方法 借助于一元函数将多元函数的问题简化.结果 由一元函数左、右导数的定义及其性质,将多元函数的方向导数转为一元函数左、右导数,从而解决了微积分学习和研究中的一个难点.结论 学习和研究微积分的过程中,可以利用已学过的较简单的知识,处理和简化较难的问题.

Aims\ To solve the problems of the directional derivative of the multivariable functions. Methods\ We can simplify multivariable function with the help of single variable function. Results\ We change the directional derivative of the multivariable functions into the left and right derivative and the progressive derivative of the singlevariable functions with the help of the definition and the property of the singlevariable functions. As a result, the difficult point in the study of the infinitesimal calculus can be solved. Conclusion\ In the process of the study of the infinitesimal calculus, we can use the simple knowledge which has been learned to simplify the more difficult contents.