Extended Formulations in Mixed-Integer Convex Programming
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1511.06710.pdf
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Author(s)
Yamangil, Emre
Bent, Russell
Lubin, Miles C
Vielma, Juan Pablo
Date Issued
May 2016
Journal
International Conference on Integer Programming and Combinatorial Optimization
Publisher
Springer-Verlag
Citation
Lubin, Miles et al. “Extended Formulations in Mixed-Integer Convex Programming.” International Conference on Integer Programming and Combinatorial Optimization (2016): 102–113. doi:10.1007/978-3-319-33461-5_9. © 2016 The Author(s)
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Author's final manuscript
Abstract
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1007/978-3-319-33461-5_9
