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Cuts for Conic Mixed-Integer Programming

  • Conference paper
Integer Programming and Combinatorial Optimization (IPCO 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4513))

Abstract

A conic integer program is an integer programming problem with conic constraints. Conic integer programming has important applications in finance, engineering, statistical learning, and probabilistic integer programming.

Here we study mixed-integer sets defined by second-order conic constraints. We describe general-purpose conic mixed-integer rounding cuts based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve continuous conic programming relaxations at the nodes of the search tree. Our preliminary computational experiments with the new cuts show that they are quite effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs.

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Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720-1777, USA

    Alper Atamtürk & Vishnu Narayanan

Authors
  1. Alper Atamtürk
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  2. Vishnu Narayanan
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Editor information

Matteo Fischetti David P. Williamson

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Atamtürk, A., Narayanan, V. (2007). Cuts for Conic Mixed-Integer Programming. In: Fischetti, M., Williamson, D.P. (eds) Integer Programming and Combinatorial Optimization. IPCO 2007. Lecture Notes in Computer Science, vol 4513. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72792-7_2

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  • DOI: https://doi.org/10.1007/978-3-540-72792-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72791-0

  • Online ISBN: 978-3-540-72792-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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