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Error Bounds for Quadratic Systems

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High Performance Optimization

Part of the book series: Applied Optimization ((APOP,volume 33))

Abstract

In this paper we consider the problem of estimating the distance from a given point to the solution set of a quadratic inequality system. We show, among other things, that a local error bound of order 1/2 holds for a system defined by linear inequalities and a single (nonconvex) quadratic equality. We also give a sharpening of Lojasiewicz’ error bound for piecewise quadratic functions. In contrast, the early results for this problem further require either a convexity or a nonnegativity assumption.

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Authors
  1. Zhi-Quan Luo
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  2. Jos F. Sturm
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Editor information

Editors and Affiliations

  1. Erasmus University, Rotterdam, The Netherlands

    Hans Frenk  & Shuzhong Zhang  & 

  2. Delft University of Technology, The Netherlands

    Kees Roos  & Tamás Terlaky  & 

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© 2000 Springer Science+Business Media Dordrecht

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Luo, ZQ., Sturm, J.F. (2000). Error Bounds for Quadratic Systems. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds) High Performance Optimization. Applied Optimization, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3216-0_16

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  • DOI: https://doi.org/10.1007/978-1-4757-3216-0_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4819-9

  • Online ISBN: 978-1-4757-3216-0

  • eBook Packages: Springer Book Archive

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