论文标题
亚级别在多面体功能的变分分析中的作用
Role of Subgradients in Variational Analysis of Polyhedral Functions
论文作者
论文摘要
了解亚级别在各种二阶变异分析结构中的作用可以帮助我们在变异分析中发现重要类别功能的新属性。主要关注多面体功能的第二个下降低和亚加密原的原源性，具有多面性铭文的功能，我们证明，选择这些概念的定义中选择了潜在的亚级别，从这些概念的定义中使用，从严格的特性属性属性属性的相对性内部，以确保多面性级别的多样性属性，亚级别的原始差异性。这使我们能够表征近端映射的连续可不同性和多面部函数莫罗包络的两次连续可不同性。我们结束了论文，证明了在其非排定溶液中的一类广义方程式的度量规律性和强度的度量规则性。
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the second subderivative and subgradient proto-derivative of polyhedral functions, functions with polyhedral epigraphs, we demonstrate that choosing the underlying subgradient, utilized in the definitions of these concepts, from the relative interior of the subdifferential of polyhedral functions ensures stronger second-order variational properties such as strict twice epi-differentiability and strict subgradient proto-differentiability. This allows us to characterize continuous differentiability of the proximal mapping and twice continuous differentiability of the Moreau envelope of polyhedral functions. We close the paper with proving the equivalence of metric regularity and strong metric regularity of a class of generalized equations at their nondegenerate solutions.
