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arXiv · 1611.07491

Mixed-integer convex representability

Miles Lubin·Ilias Zadik·Juan Pablo Vielma
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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.

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Miles Lubin, Ilias Zadik, Juan Pablo Vielma. 2017-03-08. Mixed-integer convex representability. https://doi.org/10.1007/978-3-319-59250-3_32

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