论文标题
重新访问错误范围
Error bounds revisited
论文作者
论文摘要
我们提出了一个统一的定量原始框架和双重和必要的误差结合条件，涵盖了线性和非线性，本地和全局设置。除了有足够条件的情况下，除了较低的半进入性的标准假设外，并且（在某些情况下）在必要条件的情况下，该功能不具有任何特定的结构。我们揭示了涉及错误主张的假设的作用，尤其是在基础空间中：一般度量，规范，Banach或asplund。我们采用特殊的坡度运算符集合，引入了一种简洁的形式的误差绑定条件的简洁形式，该形式可以在单个陈述中组合几种不同的断言：在完整的度量空间中的非局部和局部原始空间条件，以及在Banach和Asplund空间中的细分条件。
We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart from the standard assumptions of lower semicontinuity in the case of sufficient conditions and (in some cases) convexity in the case of necessary conditions. We expose the roles of the assumptions involved in the error bound assertions, in particular, on the underlying space: general metric, normed, Banach or Asplund. Employing special collections of slope operators, we introduce a succinct form of sufficient error bound conditions, which allows one to combine in a single statement several different assertions: nonlocal and local primal space conditions in complete metric spaces, and subdifferential conditions in Banach and Asplund spaces.
