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The MILP Road to MIQCP

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Mixed Integer Nonlinear Programming

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 154))

Abstract

This paper surveys results on the NP-hard mixed-integer quadratically constrained programming problem. The focus is strong convex relaxations and valid inequalities, which can become the basis of efficient global techniques. In particular, we discuss relaxations and inequalities arising from the algebraic description of the problem as well as from dynamic procedures based on disjunctive programming. These methods can be viewed as generalizations of techiniques for mixed-integer linear programming. We also present brief computational results to indicate the strength and computational requirements of these methods.

Author supported in part by NSF Grant CCF-0545514.

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Authors and Affiliations

  1. Department of Management Sciences, University of Iowa, Iowa City, IA, 52242-1994, USA

    Samuel Burer

  2. Axioma Inc., 8800 Roswell Road, Building B. Suite 295, Atlanta, GA, 30350, USA

    Anureet Saxena

Authors
  1. Samuel Burer
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  2. Anureet Saxena
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Correspondence to Samuel Burer .

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Editors and Affiliations

  1. , College of Engineering, University of Michigan, 2355 Bonisteel Boulevard, Ann Arbor, 48109, Michigan, USA

    Jon Lee

  2. , Mathematics and Computer Science, Argonne National Laboratory, Argonne, 60439, Illinois, USA

    Sven Leyffer

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Burer, S., Saxena, A. (2012). The MILP Road to MIQCP. In: Lee, J., Leyffer, S. (eds) Mixed Integer Nonlinear Programming. The IMA Volumes in Mathematics and its Applications, vol 154. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1927-3_13

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