论文标题
凸功能的指标和异构体
Metrics and Isometries for Convex Functions
论文作者
论文摘要
我们在$ \ mathbb {r}^n $上使用全维域引入了对称差异度量的一类功能类似物。我们表明，相对于这些指标的收敛等同于Epi-Convergence。此外，我们对某些新指标提供了所有同构的完整分类。此外，我们分别在强制凸函数和超能力凸函数的空间上引入了Hausdorff度量的两个新功能类似物，并证明与Epi-Convergence相当。
We introduce a class of functional analogs of the symmetric difference metric on the space of coercive convex functions on $\mathbb{R}^n$ with full-dimensional domain. We show that convergence with respect to these metrics is equivalent to epi-convergence. Furthermore, we give a full classification of all isometries with respect to some of the new metrics. Moreover, we introduce two new functional analogs of the Hausdorff metric on the spaces of coercive convex functions and super-coercive convex functions, respectively, and prove equivalence to epi-convergence.
