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# Welcome to the Bonmin Wiki

Bonmin (**B**asic **O**pen-source **N**onlinear **M**ixed **IN**teger 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 new Reformulation-Linearization based Branch-and-bound project is available in COIN-OR: Couenne

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

Bonmin is also available in the GAMS modeling system (since release 22.5) of . 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 instruction see GettingStarted.

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).

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. To appear in Discrete Optimization, in press.

## Authors of the code

Project manager: Pierre Bonami

### Contributors

- Pietro Belotti, (Carnegie Mellon University),
- Pierre Bonami, (Université de la Méditérannée)
- Claudia D'Ambrosio (Università di Bologna),
- John J. Forrest (IBM Copr.),
- Lazlo Ladanyi (IBM Copr.),
- Carl Laird, (Carnegie Mellon University),
- Jon Lee (IBM Copr.),
- Francois Margot (Carnegie Mellon University),
- Stefan Vigerske (Humboldt-University, Berlin),
- 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.

## Project Links

- COIN-OR Initiative
- IBM CMU Open Source MINLP project
- Bonmin mailing list
- coin-discuss mailing list
- Report a bug
- ReleasesHistory page
- WishList wiki page
- HintTricks wiki page
- DevelopperWiki page

## 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 Stefan Vigerske provides some benchmark of various MINLP solver available in GAMS including Bonmin.

## 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:

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.