Nonlinear Error Bounds via a Change of Function

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• 作者：Dominique Azé ; Jean-Noël Corvellec
• 关键词：Nonlinear error bounds ; Asymptotically well ; behaved functions ; Descent methods in optimization
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：172
• 期：1
• 页码：9-32
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

This work can be seen as a sequel to our previous paper, which dealt with local nonlinear error bounds for lower semicontinuous functions on complete metric spaces, based on estimates of the strong slope of the function through the distance to a sublevel set. Here, we consider estimates of the strong slope through the values of the function, and we provide characterizations of nonlinear local and global error bounds that are again obtained by a reduction to the linear case. Our main tool is a simple chain rule for the strong slope. We provide several examples showing that recent results in the literature can be recaptured from our general framework.