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Abstract
We present a review of available tools for solving mixed integer nonlinear programming problems. Our aim is to give the reader a flavor of the difficulties one could face and to discuss the tools one could use to try to overcome such difficulties.
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Notes
Note that we do not consider MINLPs that can be exactly reformulated as MILP problems.
Ifk=1, no fixing is performed.
A pseudo-convex MINLP is an MINLP involving pseudo-convex functions. Informally, a function is pseudo-convex if behaves like a convex function with respect to finding its local minima, but need not actually be convex, see, e.g., Mangasarian (1965).
The development ofLAGO is currently ceased but the software is open-source, so we prefer to keep it into the list because future development is possible.
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Acknowledgements
We are grateful to Silvano Martello for precious suggestions. Thanks are also due to Stefan Vigerske for useful comments and discussions.
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CNRS LIX, Ecole Polytechnique, 91128, Palaiseau, France
Claudia D’Ambrosio
DEI, University of Bologna, viale Risorgimento 2, 40136, Bologna, Italy
Andrea Lodi
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This is an updated version of the paper that appeared in4OR, 9(4), 329–349 (2011).
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D’Ambrosio, C., Lodi, A. Mixed integer nonlinear programming tools: an updated practical overview.Ann Oper Res204, 301–320 (2013). https://doi.org/10.1007/s10479-012-1272-5
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