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An Algorithmic Framework for MINLP with Separable Non-Convexity

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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

We present an algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems in which the non-convexity in the objective and constraint functions is manifested as the sum of non-convex univariate functions. We employ a lower bounding convex MINLP relaxation obtained by approximating each non-convex function with a piecewise-convex underestimator that is repeatedly refined. The algorithm is implemented at the level of a modeling language. Favorable numerical results are presented.

AMS(MOS) subject classifications. 65K05, 90C11, 90C26, 90C30.

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Author information

Authors and Affiliations

  1. Department of ECSS, University of Bologna, Bologna, Italy

    Claudia D’Ambrosio

  2. Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Jon Lee

  3. IBM T.J. Watson Research Center, Hawthorne, NY, 10598, USA

    Andreas Wächter

Authors
  1. Claudia D’Ambrosio
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  2. Jon Lee
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  3. Andreas Wächter
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Corresponding author

Correspondence to Claudia D’Ambrosio .

Editor information

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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D’Ambrosio, C., Lee, J., Wächter, A. (2012). An Algorithmic Framework for MINLP with Separable Non-Convexity. 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_11

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