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A sufficient condition for lower semicontinuity of solution sets of systems of convex inequalities

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Sensitivity, Stability and Parametric Analysis

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 21))

Abstract

This paper develops a sufficient condition for the lower semicontinuity of the solution set mapping of a system of convex inequalities, when the data are subjected to small perturbations. The condition established here does not include regularity assumptions of the Slater type. Possibilities of simplifying the results and an application to parametric optimization problems are discussed.

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Authors and Affiliations

  1. Sektion Mathematik, Humboldt-Universität zu Berlin, 1086, Berlin, GDR

    Diethard Klatte

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  1. Diethard Klatte
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Anthony V. Fiacco

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© 1984 The Mathematical Programming Society, Inc.

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Klatte, D. (1984). A sufficient condition for lower semicontinuity of solution sets of systems of convex inequalities. In: Fiacco, A.V. (eds) Sensitivity, Stability and Parametric Analysis. Mathematical Programming Studies, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121216

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  • DOI: https://doi.org/10.1007/BFb0121216

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00912-9

  • Online ISBN: 978-3-642-00913-6

  • eBook Packages: Springer Book Archive

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