Mixed-Integer Convex Representability
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1611.07491.pdf
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Author(s)
Lubin, Miles C
Zadik, Ilias
Vielma, Juan Pablo
Date Issued
May 2017
Journal
International Conference on Integer Programming and Combinatorial Optimization
Publisher
Springer-Verlag
Citation
Lubin, Miles et al. “Mixed-Integer Convex Representability.” International Conference on Integer Programming and Combinatorial Optimization (2017): 392–404. doi:10.1007/978-3-319-59250-3_32. © 2017 The Author(s)
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Author's final manuscript
Abstract
We consider the question of which nonconvex sets can be represented exactly as the feasible sets of mixed-integer convex optimization problems. We state the first complete characterization for the case when the number of possible integer assignments is finite. We develop a characterization for the more general case of unbounded integer variables together with a simple necessary condition for representability which we use to prove the first known negative results. Finally, we study representability of subsets of the natural numbers, developing insight towards a more complete understanding of what modeling power can be gained by using convex sets instead of polyhedral sets; the latter case has been completely characterized in the context of mixed-integer linear optimization.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/978-3-319-59250-3_32
