Nonlinear local error bounds via a change of metric
Nonlinear local error bounds via a change of metric
复制标题
通过度量的变化实现非线性局部误差范围
DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
J. Corvellec
中科院分区：
文献类型：
--
作者：
D. Azé;J. Corvellec
在这项工作中，我们改进了第二作者和V. Motreanu [Math. Program。114（2008），291-319]的非线性误差界的下连续函数在完整的度量空间，一种方法在于减少非线性的情况下，通过改变度量的线性。这种改进基本上是一种技术改进，它允许以适当的方式处理局部误差范围。我们提出了一些后果的一般结果的框架中的经典非光滑分析，涉及Banach空间和次微分算子。特别是，我们描述了一个函数的局部二次增长和度量正则性的次微分之间的连接。
In this work, we improve the approach of the second author and V. Motreanu [Math. Program. 114 (2008), 291–319] to nonlinear error bounds for lower semicontinuous functions on complete metric spaces, an approach consisting in reducing the nonlinear case to the linear one through a change of metric. This improvement is basically a technical one, and it allows dealing with local error bounds in an appropriate way. We present some consequences of the general results in the framework of classical nonsmooth analysis, involving Banach spaces and subdifferential operators. In particular, we describe connections between local quadratic growth of a function and metric regularity of its subdifferential.