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Minotaur: a mixed-integer nonlinear optimization toolkit

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Abstract

We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting extensions that we implement in our framework and demonstrate their impact on solution times. Without a flexible framework that enables structure exploitation, finding global solutions to difficult nonconvex MINLP problems will remain out of reach for many applications.

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Acknowledgements

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under contract DE-AC02-06CH11357. This work was also supported by the U.S. Department of Energy under Grant DE-FG02-05ER25694.

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Authors and Affiliations

  1. Industrial Engineering and Operations Research, IIT Bombay, Mumbai, 400076, India

    Ashutosh Mahajan

  2. Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, 60439, USA

    Sven Leyffer & Todd Munson

  3. Department of Industrial and Systems Engineering, University of Wisconsin-Madison, Madison, WI, 53706, USA

    Jeff Linderoth & James Luedtke

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  1. Ashutosh Mahajan
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Mahajan, A., Leyffer, S., Linderoth, J. et al. Minotaur: a mixed-integer nonlinear optimization toolkit. Math. Prog. Comp. 13, 301–338 (2021). https://doi.org/10.1007/s12532-020-00196-1

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