分段线性二次函数的ε-次微分的可视化
Visualization of the ε-Subdifferential of Piecewise Linear-Quadratic Functions
摘要：
显式计算一个真函数的ε-次微分等价于计算一个凸函数的水平集，即共轭减一个线性函数。由此产生的理论算法适用于类（凸单变量）分段线性二次函数，现有的数值库允许实际计算。我们可视化的结果，在一个原始的，对偶的，和次微分的意见，通过几个数值例子。我们还提供了一个可视化的Brøndsted-Rockafellar定理。
英文摘要：
Computing explicitly the ε-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) piecewise linear-quadratic functions for which existing numerical libraries allow practical computations. We visualize the results in a primal, dual, and subdifferential views through several numerical examples. We also provide a visualization of the Brøndsted-Rockafellar Theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
