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A geometric approach to cut-generating functions

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Abstract

The cutting-plane approach to integer programming was initiated more than 40 years ago: Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron. This line of research was left dormant for several decades until relatively recently, when a paper of Andersen, Louveaux, Weismantel and Wolsey generated renewed interest in the corner polyhedron and intersection cuts. Recent developments rely on tools drawn from convex analysis, geometry and number theory, and constitute an elegant bridge between these areas and integer programming. We survey these results and highlight recent breakthroughs in this area.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, MD, USA

    Amitabh Basu

  2. Dipartimento di Matematica, Università degli Studi di Padova, Padua, Italy

    Michele Conforti & Marco Di Summa

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  1. Amitabh Basu
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  2. Michele Conforti
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  3. Marco Di Summa
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Correspondence to Michele Conforti.

Additional information

Michele Conforti and Marco Di Summa were supported by the Grant “Progetto di Ateneo 2013” of the University of Padova.

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Basu, A., Conforti, M. & Di Summa, M. A geometric approach to cut-generating functions. Math. Program. 151, 153–189 (2015). https://doi.org/10.1007/s10107-015-0890-5

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