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Welcome to the Bonmin Wiki

Bonmin (Basic Open-source Nonlinear Mixed INteger programming) is an experimental open-source C++ code for solving general MINLP (Mixed Integer NonLinear Programming) problems of the form:

   min     f(x)

s.t.       g_L <= g(x) <= g_U
           x_L <=  x   <= x_U
           x_i in Z for all i in I and,
           x_i in R for all i not in I.

where f(x): R^n --> R, g(x): R^n --> R^m are twice continuously differentiable functions and I is a subset of {1,..,n}.

Bonmin features several algorithms

  • B-BB is a NLP-based branch-and-bound algorithm,
  • B-OA is an outer-approximation decomposition algorithm,
  • B-QG is an implementation of Quesada and Grossmann's branch-and-cut algorithm,
  • B-Hyb is a hybrid outer-approximation based branch-and-cut algorithm.

The algorithms in Bonmin are exact when the functions f and g are convex; in the case where f or g or both are non-convex they are heuristics.

For global optima of non-convex MINLPs, a Reformulation-Linearization based Branch-and-bound project is available in COIN-OR: Couenne

Bonmin is distributed under the Eclipse Public License (EPL) on COIN-OR. The EPL is a license approved by the OSI (Open Source Initiative), thus Bonmin is OSI Certified Open Source Software.

You can use Bonmin through the NEOS web interface and through the JuMP modeling language.

Bonmin is also available in the AMPL and GAMS modeling systems. Without buying a license, these systems work as a demo with limited capabilities. AMPL/Bonmin binaries are available for download.

There is also an interface to MATLAB OPTI Toolbox under development by Jonathan Currie.

For short download and installation instruction see GettingStarted. Binaries are available as part of the CoinAll binaries.

More information and links can be found on Bonmin homepage. More on installation and usage can be found in the Bonmin User's Manual ( html, pdf).

Description of the underlying algorithms in Bonmin can be found in: P. Bonami, L.T. Biegler, A.R. Conn, G. Cornuejols, I.E. Grossmann, C.D. Laird, J. Lee, A. Lodi, F. Margot, N.Sawaya and A. Waechter, An Algorithmic Framework for Convex Mixed Integer Nonlinear Programs. Discrete Optimization. 5(2):186-204, 2008.

Authors of the code

Project manager: Pierre Bonami



The code has been developed as part of a collaboration between Carnegie Mellon University and IBM Research to study new algorithms for MINLPs. Credit should be given to our colleagues in this collaboration (which are not already cited as contributors): Larry T. Biegler, Andrew R Conn, Gerard Cornuejols, Ignacio E. Grossmann, Andrea Lodi and Nick Sawaya. They all took a very significant part in every aspects of the work and research which lead to Bonmin.

We, also, warmly thank Jeff Linderoth and Hans Mittelmann for their help on installing Bonmin on NEOS and Stefan Vigerske for his work on linking Bonmin with GAMS.

Improve this page, report a bug, contribute to Bonmin

As an open-source code, contributions to Bonmin are welcome. To submit a contribution to Bonmin please follow the COIN-OR guidelines.

The preferred way to report a bug is to use the ticket system. To report a bug using this system:

  1. Register and login,
  2. Report a bug.

As all Wiki pages, this page is editable, this means that you can modify the contents of this page simply by using your web-browser. First register and login then simply click on the "Edit this page" link at the bottom of the page. WikiFormatting will give you a detailed description of available Wiki formatting commands.

Last modified 20 months ago Last modified on Feb 28, 2020 11:42:58 AM