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Title: Couenne  
Author: World Heritage Encyclopedia
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Subject: FICO Xpress, SNOPT, APMonitor, AMPL, Numerical software
Collection: Articles Created Via the Article Wizard, Mathematical Optimization Software, Numerical Software
Publisher: World Heritage Encyclopedia


Stable release 0.5.2
Development status Active
Written in C++ (programming language)
Operating system Cross-platform

Couenne (Convex Over and UnderENvelopes for Nonlinear Estimation) is an open source library for solving global optimization problems, also known as mixed integer nonlinear optimization problems.[1] A global optimization problem requires to minimize a 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[2] and provides a linear programming approximation of any nonconvex optimization problem.[3]

Couenne is an implementation of a branch-and-bound where every subproblem is solved by constructing a 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 the AMPL .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 terminates without interruption.

The development of Couenne was started in 2006 within a collaboration between IBM and Carnegie Mellon University. It is open source and is currently distributed under the Eclipse Public License v1.0.

The source code is available for download in the COIN-OR repository and on Github. Couenne uses other packages both in COIN-OR (CBC, CLP, COIN-OR OSI, COIN-OR Bonmin, COIN-OR Cgl, Ipopt) and outside (Lapack, Blas, Mumps, Nauty, SCIP, SoPlex).

See also

  • BARON - A commercial solver for MINLP developed by Nick Sahinidis and others;
  • LINDO - A suite comprising LindoGlobal for solving global optimization problems.
  • SCIP - A freely available solver for MILP, MIQCQP, and global optimization problems;


  1. ^ 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.
  2. ^ 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.
  3. ^ 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.

External links

  • Couenne homepage
  • Source code (trunk)
  • Project page
  • User manual
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