An algorithmic framework for convex mixed integer nonlinear programs

Pierre Bonami, Lorenz T. Biegler, Andrew R. Conn, Gérard Cornuéjols, Ignacio E. Grossmann, Carl D. Laird, Jon Lee, Andrea Lodi, François Margot, Nicolas Sawaya, Andreas Wächter*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

447 Scopus citations

Abstract

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, are proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported. Both the library of mixed integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried out, and a version of the software used are publicly available.

Original languageEnglish (US)
Pages (from-to)186-204
Number of pages19
JournalDiscrete Optimization
Volume5
Issue number2
DOIs
StatePublished - May 2008

Keywords

  • Branch-and-bound
  • MINLP test problems
  • Mixed integer nonlinear programming
  • Open-source
  • Outer-approximation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

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