# `BONMIN` Users' Manual

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### References

[1] K. Abhishek, S. Leyffer, and J. T. Linderoth. FilMINT: An outer-approximation-based solver for nonlinear mixed integer programs. Preprint ANL/MCS-P1374-0906, Mathematics and Computer Science Division, Argonne National Laboratory, 2006.

[2] P. Bonami, A. Wächter, L.T. Biegler, A.R. Conn, G. Cornuéjols, I.E. Grossmann, C.D. Laird, J. Lee, A. Lodi, F. Margot and N. Sawaya. An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optimization 5:186–204, 2008.

[3] P. Bonami, G. Cornuéjols, A. Lodi, and F. Margot. A feasibility pump for mixed integer nonlinear programs. Mathematical Programming, 119 (2009), pp. 331–352.

[4] P. Bonami and J. Gonçalves. Primal heuristics for mixed integer nonlinear programs. Research Report, IBM T. J. Watson Research Center, Yorktown, USA, September 2008.

[5] P. Bonami, M. Klnç and J. Linderoth. Algorithms and Software for Convex Mixed Integer Nonlinear Programs. Technical Report #1664, Computer Sciences Department, University of Wisconsin-Madison, 2009.

[6] M. Duran and I.E. Grossmann. An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming, 36:307–339, 1986.

[7] O.K. Gupta and V. Ravindran. Branch and bound experiments in convex nonlinear integer programming. Management Science, 31:1533–1546, 1985.

[8] R. Fletcher and S. Leyffer. Solving mixed integer nonlinear programs by outer approximation. Mathematical Programming, 66:327–349, 1994.

[9] R. Fletcher and S. Leyffer. User manual for filterSQP. University of Dundee Numerical Analysis Report NA-181, 1998.

[10] D.M. Gay. Writing .nl files. Sandia National Laboratories, Technical Report No. 2005-7907P, 2005.

[11] I. Quesada and I.E. Grossmann. An LP/NLP based branched and bound algorithm for convex MINLP optimization problems. Computers and Chemical Engineering, 16:937–947, 1992.

[12] R. Fourer and D.M. Gay and B.W. Kernighan. AMPL: A Modeling Language for Mathematical Programming, Second Edition, Duxbury Press Brooks Cole Publishing Co., 2003.

[13] J. Nocedal, A. Wächter, and R. A. Waltz. Adaptive Barrier Strategies for Nonlinear Interior Methods. Research Report RC 23563, IBM T. J. Watson Research Center, Yorktown, USA (March 2005; revised January 2006)

[14] A. Wächter and L. T. Biegler. On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming. Mathematical Programming 106(1), pp. 25-57, 2006