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Submodular functions and convexity

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Mathematical Programming The State of the Art

Abstract

In “continuous” optimization convex functions play a central role. Besides elementary tools like differentiation, various methods for finding the minimum of a convex function constitute the main body of nonlinear optimization. But even linear programming may be viewed as the optimization of very special (linear) objective functions over very special convex domains (polyhedra). There are several reasons for this popularity of convex functions:

  • Convex functions occur in many mathematical models in economy, engineering, and other sciencies. Convexity is a very natural property of various functions and domains occuring in such models; quite often the only non-trivial property which can be stated in general.

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Author information

Authors and Affiliations

  1. Department of Analysis I, Eötvös Loránd University, Múzeum krt. 6-8, H-1088, Budapest, Hungary

    L. Lovász

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  1. L. Lovász
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Editor information

Editors and Affiliations

  1. Institut für Ökonometrie und Operations Research, Universität Bonn, Nassestraße 2, D-5300, Bonn 1, Germany

    Achim Bachem  & Bernhard Korte  & 

  2. Lehrstuhl für Angewandte Mathematik II, Universität Augsburg, Memminger Straße 6, D-8900, Augsburg, Germany

    Martin Grötschel

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© 1983 Springer-Verlag Berlin Heidelberg

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Lovász, L. (1983). Submodular functions and convexity. In: Bachem, A., Korte, B., Grötschel, M. (eds) Mathematical Programming The State of the Art. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68874-4_10

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  • DOI: https://doi.org/10.1007/978-3-642-68874-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-68876-8

  • Online ISBN: 978-3-642-68874-4

  • eBook Packages: Springer Book Archive

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