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Algorithms and Software for Convex Mixed Integer Nonlinear Programs

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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 provides a survey of recent progress and software for solving convex Mixed Integer Nonlinear Programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in recent years. By exploiting analogies to well-known techniques for solving Mixed Integer Linear Programs and incorporating these techniques into software, significant improvements have been made in the ability to solve these problems.

Supported by ANR grand BLAN06-1-138894.

The work of the second and third authors is supported by the US Department of Energy under grants DE-FG02-08ER25861 and DE-FG02-09ER25869, and the National Science Foundation under grant CCF-0830153.

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  1. Laboratoire d’Informatique Fondamentale de Marseille, CNRS, Aix-Marseille Universités, Parc Scientifique et Technologique de Luminy, 163 avenue de Luminy - Case 901, F-13288, Marseille Cedex 9, France

    Pierre Bonami

  2. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, 1513 University Ave., Madison, WI, 53706, USA

    Mustafa Kilinç & Jeff Linderoth

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  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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Bonami, P., Kilinç, M., Linderoth, J. (2012). Algorithms and Software for Convex Mixed Integer Nonlinear Programs. 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_1

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