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Nonlinear Error Bounds via a Change of Function

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Abstract

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.

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Authors and Affiliations

  1. Université Paul Sabatier, Toulouse, France

    Dominique Azé

  2. Université de Perpignan Via Domitia, Perpignan, France

    Jean-Noël Corvellec

Authors
  1. Dominique Azé
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  2. Jean-Noël Corvellec
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Correspondence to Jean-Noël Corvellec.

Additional information

Communicated by Viorel Barbu.

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Azé, D., Corvellec, JN. Nonlinear Error Bounds via a Change of Function. J Optim Theory Appl 172, 9–32 (2017). https://doi.org/10.1007/s10957-016-1001-3

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  • DOI: https://doi.org/10.1007/s10957-016-1001-3

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