An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs

Ignacio Grossmann, Carnegie Mellon University
Pierre Bonami, Carnegie Mellon University
Lorenz Biegler, IBM
Andrew Conn, Carnegie Mellon University
Gerard Cornuejols, Carnegie Mellon University
Carl Laird, IBM
Jon Lee, Carnegie Mellon University
Andrea Lodi, Carnegie Mellon University
Francois Margot, Carnegie Mellon University
Nicolas Sawaya, IBM
Andreas Wachter, IBM

Abstract or Description

This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch and bound and polyhedral outer approximation are the two extreme cases, is proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported, and a library of mixed integer nonlinear problems that exhibit convex continuous relaxations is made publicly available.