Polyhedral approximation in mixed-integer convex optimization
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10107_2017_1191_ReferencePDF.pdf
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Author(s)
Yamangil, Emre
Bent, Russell
Lubin, Miles C
Vielma Centeno, Juan Pablo
Date Issued
September 2017
Journal
Mathematical Programming
Publisher
Springer-Verlag
Citation
Lubin, Miles, Emre Yamangil, Russell Bent, and Juan Pablo Vielma. “Polyhedral Approximation in Mixed-Integer Convex Optimization.” Mathematical Programming 172, no. 1–2 (September 14, 2017): 139–168.
Version
Author's final manuscript
Abstract
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro.
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/s10107-017-1191-y
