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Error Bounds: Necessary and Sufficient Conditions

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Abstract

The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.

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Author information

Authors and Affiliations

  1. Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 11567, Prague 1, Czech Republic

    Marian J. Fabian

  2. Weierstrass Institute for Applied Analysis and Stochastics, 10117, Berlin, Germany

    René Henrion

  3. School of Information Technology and Mathematical Sciences, Centre for Informatics and Applied Optimization, University of Ballarat, POB 663, Ballarat, Vic, 3350, Australia

    Alexander Y. Kruger

  4. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, 18208, Prague, Czech Republic

    Jiří V. Outrata

Authors
  1. Marian J. Fabian
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  2. René Henrion
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  3. Alexander Y. Kruger
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  4. Jiří V. Outrata
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Corresponding author

Correspondence to Alexander Y. Kruger.

Additional information

The research of Marian J. Fabian was supported by Institutional Research Plan of the Academy of Sciences of Czech Republic AVOZ 101 905 03, and by GAČR 201/07/0394.

The research of René Henrion was supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.

The main structure of the article was developed during Alexander Y. Kruger’s stay at the Institute of Information Theory and Automation of the Academy of Sciences of the Czech Republic in July–August 2008; this author is grateful to the Institute for support and hospitality.

The research of Jiří V. Outrata was supported by IAA 100750802 of the Grant Agency of the Czech Academy of Sciences.

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Fabian, M.J., Henrion, R., Kruger, A.Y. et al. Error Bounds: Necessary and Sufficient Conditions. Set-Valued Anal 18, 121–149 (2010). https://doi.org/10.1007/s11228-010-0133-0

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  • DOI: https://doi.org/10.1007/s11228-010-0133-0

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