Small and strong formulations for unions of convex sets from the Cayley embedding
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Author(s)
Vielma Centeno, Juan Pablo
Date Issued
March 2018
Journal
Mathematical Programming
Publisher
Springer Nature America, Inc
Citation
Vielma, Juan Pablo. “Small and Strong Formulations for Unions of Convex Sets from the Cayley Embedding.” Mathematical Programming (March 30, 2018).
Version
Author's final manuscript
Abstract
There is often a significant trade-off between formulation strength and size in mixed integer programming (MIP). When modelling convex disjunctive constraints (e.g. unions of convex sets) this trade-off can be resolved by adding auxiliary continuous variables. However, adding these variables can result in a deterioration of the computational effectiveness of the formulation. For this reason, there has been considerable interest in constructing strong formulations that do not use continuous auxiliary variables. We introduce a technique to construct formulations without these detrimental continuous auxiliary variables. To develop this technique we introduce a natural nonpolyhedral generalization of the Cayley embedding of a family of polytopes and show it inherits many geometric properties of the original embedding. We then show how the associated formulation technique can be used to construct small and strong formulation for a wide range of disjunctive constraints. In particular, we show it can recover and generalize all known strong formulations without continuous auxiliary variables.
MIT Department
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/S10107-018-1258-4
