Paper Info
Title
Polyhedral approximation in mixed-integer convex optimization.
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.
Year
DOI
Venue
2018
10.1007/s10107-017-1191-y
Math. Program.
Keywords
Field
DocType
Convex MINLP,Outer approximation,Disciplined convex programming,90–08,90C11,90C25
Discrete mathematics,Mathematical optimization,Nonlinear programming,Subderivative,Conic optimization,Proper convex function,Ellipsoid method,Convex optimization,Convex analysis,Linear matrix inequality,Mathematics
Journal
Volume
Issue
ISSN
172
1-2
0025-5610
Citations 
PageRank 
References 
6
0.47
21
Authors
4
Name
Order
Citations
PageRank
Miles Lubin118413.98
Emre Yamangil2293.62
Russell Bent333526.14
Juan Pablo Vielma433425.34