论文标题
分段仿射功能的非本地误差界限
Nonlocal error bounds for piecewise affine functions
论文作者
论文摘要
该论文致力于对非convex分段仿射函数的非本地误差界限的详细分析。我们既改进了此类功能的误差范围的现有结果，并为分段仿射功能提供了全新的必要条件和/或足够的条件，以在各种类型的有界和无限的集合上绑定错误。特别是，我们表明，任何分段仿射函数都在任意界集的集合上绑定一个错误，并提供了几种易于验证的足够条件，以使此类函数在无限制集合上绑定错误。我们还为分段仿射函数提供了一般必要和充分的条件，以使多面体集合的有限结合（尤其是具有全局误差绑定）绑定的错误，其派生揭示了分段集合仿射功能的阶段集合和经济衰退功能的结构。
The paper is devoted to a detailed analysis of nonlocal error bounds for nonconvex piecewise affine functions. We both improve some existing results on error bounds for such functions and present completely new necessary and/or sufficient conditions for a piecewise affine function to have an error bound on various types of bounded and unbounded sets. In particular, we show that any piecewise affine function has an error bound on an arbitrary bounded set and provide several types of easily verifiable sufficient conditions for such functions to have an error bound on unbounded sets. We also present general necessary and sufficient conditions for a piecewise affine function to have an error bound on a finite union of polyhedral sets (in particular, to have a global error bound), whose derivation reveals a structure of sublevel sets and recession functions of piecewise affine functions.
