Extended Formulations in Mixed-integer Convex Programming

Event Sponsor: 
Mathematics and Computing Science - LANS Seminar
Start Date: 
Dec 10 2015 - 1:00pm
Building/Room: 
Building 240/Room 1406-1407
Location: 
Argonne National Laboratory
Speaker(s): 
Miles Lubin
Speaker(s) Title: 
Massachusetts Institute of Technology
Host: 
Cosmin Petra

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 nearly 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.

Miscellaneous Information: 

Coffee and Goodies will be served.

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