广义拉格朗日定理
Generalized Lagrange Theorem
AI总结：
本文推广经典拉格朗日中值定理，针对连续多变量实值函数，提出用双序列切锥代替导数，证明了Rolle和Lagrange型结果，并与Clarke次微分及法锥方法进行了比较。
摘要：
本文致力于经典拉格朗日中值定理的可能推广。我们考虑一个仅假设为连续的多变量实值函数。核心概念是用所谓的双序列切锥代替导数的概念。我们首先证明Rolle和Lagrange型结果，然后转向在Lipschitz函数情形下将该锥与Clarke次微分进行比较。我们还研究了使用法锥的方法。
英文摘要：
The present paper is devoted to possible generalizations of the classic Lagrange Mean Value Theorem. We consider a real-valued function of several variables that is only assumed to be continuous. The main concept is to replace the notion of the derivative by the so called bisequential tangent cone. We first prove Rolle and Lagrange type results and then we turn to comparing this cone with the Clarke subdifferential in the case of a Lipschitz function. We also investigate an approach using normal cones.
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