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Generalized Convexity, Generalized Monotonicity: Recent Results pp 75–110Cite as

Error Bounds for Convex Inequality Systems

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 27))

Abstract

Using convex analysis, this paper gives a systematic and unified treatment for the existence of a globed error bound for a convex inequality system. We establish a necessary and sufficient condition for a closed convex set defined by a closed proper convex function to possess a globed error bound in terms of a natural residual. We derive many special cases of the main characterization, including the case where a Slater assumption is in place. Our results show clearly the essential conditions needed for convex inequality systems to satisfy global error bounds; they unify and extend a large number of existing results on global error bounds for such systems.1

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Author information

Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    Adrian S. Lewis

  2. Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland, 21218-2682, USA

    Jong-Shi Pang

Authors
  1. Adrian S. Lewis
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  2. Jong-Shi Pang
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Editor information

Editors and Affiliations

  1. Université Blaise Pascal, Clermont-Ferrand, France

    Jean-Pierre Crouzeix

  2. Universitat Autònoma de Barcelona, Barcelona, Spain

    Juan-Enrique Martinez-Legaz

  3. Université d’Avignon, Avignon, France

    Michel Volle

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© 1998 Kluwer Academic Publishers

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Lewis, A.S., Pang, JS. (1998). Error Bounds for Convex Inequality Systems. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_3

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  • DOI: https://doi.org/10.1007/978-1-4613-3341-8_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3343-2

  • Online ISBN: 978-1-4613-3341-8

  • eBook Packages: Springer Book Archive

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