Bonmin 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.

You can **try Bonmin** through the NEOS web interface.

Bonmin is also available in the latest release (22.5) of the GAMS modeling system. The system is available for download from GAMS. Without buying a license it works as a demo with limited capabilities.

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

For short download and installation (from sources) instruction see GettingStarted.

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

More information on 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. IBM Research Report RC23771, Oct. 2005.

## Authors of the code

Project manager: Pierre Bonami

### Contributors

- Pietro Belotti, (Carnegie Mellon University),
- Pierre Bonami, (LIF, Université de la Méditéranée)
- John J. Forrest (IBM Copr.),
- Lazlo Ladanyi (IBM Copr.),
- Carl Laird, (Carnegie Mellon University),
- Jon Lee (IBM Copr.)
- Francois Margot (Carnegie Mellon University)
- Andreas Waechter (IBM Copr.)

## Acknowledgments

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 GAMSLinks.

## External Links

- NEOS provides a web-interface to Bonmin and various other solvers.
- http://plato.asu.edu/ftp/miqp.html Hans Mittelman provides some independent benchmark comparing Bonmin to other MINLP solvers on problems with only quadratic constraints or objective.
- http://www.coin-or.org/GAMSlinks/benchmarks/index.html#minlp Stefan Vigerske provides some benchmark of various MINLP solver available in GAMS including Bonmin.

## Contribute to Bonmin, report a bug

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: