View source for Software:Couenne

{{Infobox software
| name                   = Couenne
| latest release version = 0.5.6
| programming language   = [[C++]]
| operating system       = Cross-platform
| website                = {{URL|https://github.com/coin-or/Couenne}}
}}

'''Convex Over and Under ENvelopes  for Nonlinear Estimation''' ('''Couenne''') is an [[Open-source software|open-source]] library for solving [[Global optimization|global optimization]] problems, also termed mixed integer nonlinear optimization problems.<ref>P. Belotti, C. Kirches, S. Leyffer, J. Linderoth, J. Luedtke and A. Mahajan (2013). Mixed-integer nonlinear optimization. Acta Numerica, 22, pp 1-131. doi:10.1017/S0962492913000032. http://journals.cambridge.org/abstract_S0962492913000032</ref> A global optimization problem requires to minimize a [[Function (mathematics)|function]], called objective function, subject to a set of constraints. Both the objective function and the constraints might be nonlinear and nonconvex. For solving these problems, Couenne uses a reformulation procedure<ref>M. Tawarmalani, N.V. Sahinidis. Convexification and global optimization in continuous and mixed-integer nonlinear programming: theory, algorithms, software, and applications. Vol. 65. Springer Science & Business Media, 2002.</ref> and provides a [[Linear programming|linear programming]] approximation of any nonconvex optimization problem.<ref>P. Belotti, J. Lee, L. Liberti, F. Margot, & A. Wächter (2009), Branching and bounds tightening techniques for non-convex MINLP. Optimization Methods & Software, 24(4-5), 597-634.</ref>

Couenne is an implementation of a branch-and-bound where every subproblem is solved by constructing a [[Linear programming|linear programming]] relaxation to obtain a lower bound. Branching may occur at both continuous and integer variables, which is necessary in global optimization problems. It requires the input to be specified in A Mathematical Programming Language ([[Software:AMPL|AMPL]]) [[Nl (format)|.nl format]], so as to be used from AMPL, and writes as an output a file .sol containing the best solution found until that moment (if the optimization is interrupted) or the global optimum if it completes without interruption.

The development of Couenne began in 2006 within a collaboration between [[Company:IBM|IBM]] and [[Organization:Carnegie Mellon University|Carnegie Mellon University]]. It is [[Open-source software|open-source software]] and is currently released under the [[Software:Eclipse Public License|Eclipse Public License]] v1.0.

The source code is available for download in the Computational Infrastructure for Operations Research [[Organization:COIN-OR|COIN-OR]] repository and on GitHub. Couenne uses other packages both in COIN-OR ([[Organization:COIN-OR#CBC|CBC]], CLP, COIN-OR OSI, COIN-OR Bonmin, COIN-OR Cgl, Interior Point OPTimizer ([[Software:IPOPT|IPOPT]])) and outside (LAPACK, [[Software:Basic Linear Algebra Subprograms|Basic Linear Algebra Subprograms]] (BLAS), MUltifrontal Massively Parallel sparse direct Solver ([[Software:MUMPS|MUMPS]]), Nauty, Solving Constraint Integer Programs ([[Software:SCIP (optimization software)|SCIP]]), SoPlex).

==See also==
* [[Software:BARON|BARON]] – a commercial solver for MINLP developed by Nick Sahinidis and others
* [[Software:LINDO|LINDO]] – a suite comprising LindoGlobal for solving global optimization problems
* [[Software:Octeract Engine|Octeract Engine]] – a commercial massively parallel local and global MINLP solver
* [[Software:SCIP (optimization software)|SCIP]] – a freely available solver for MILP, MIQCQP, and [[Global optimization|global optimization]] problems

== References ==
{{Reflist}}

== External links ==
* [https://projects.coin-or.org/Couenne/browser/trunk Source code (trunk)]
* [https://web.archive.org/web/20131029190415/https://projects.coin-or.org/Couenne Project page]
* [https://projects.coin-or.org/Couenne/export/974/trunk/Couenne/doc/couenne-user-manual.pdf User manual]

{{Mathematical optimization software}}

[[Category:Mathematical optimization software]]
[[Category:Numerical software]]

{{Sourceattribution|Couenne}}