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On the Complexity of Nonlinear Mixed-Integer Optimization

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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 is a survey on the computational complexity of nonlinear mixedinteger optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained fully polynomial time approximation schemes in fixed dimension, and to strongly polynomialtime algorithms for special cases.

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Authors and Affiliations

  1. Dept. of Mathematics, University of California, Davis, One Shields Avenue, Davis, CA, 95616, USA

    Matthias Köppe

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  1. Matthias Köppe
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Correspondence to Matthias Köppe .

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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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Köppe, M. (2012). On the Complexity of Nonlinear Mixed-Integer Optimization. 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_19

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