Modified Extended Cutting Plane Algorithm for Mixed Integer Nonlinear Programming

  • Wendel MeloEmail author
  • Marcia Fampa
  • Fernanda Raupp
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)


In this work, we propose a modification on the Extended Cutting Plane algorithm (ECP) that solves convex mixed integer nonlinear programming problems. Our approach, called Modified Extended Cutting Plane (MECP), is inspired on the strategy of updating the set of linearization points in the Outer Approximation algorithm (OA). Computational results over a set of 343 test instances show the effectiveness of the proposed method MECP, which outperforms ECP and is competitive to OA.


Mixed integer nonlinear programming Extended cutting plane Outer approximation 


  1. 1.
    The MOSEK optimization software. Software.
  2. 2.
    Bonami, P., Kilinç, M., Linderoth, J.: Algorithms and software for convex mixed integer nonlinear programs. Technical Report 1664, Computer Sciences Department, University of Wisconsin-Madison (2009)Google Scholar
  3. 3.
    CMU-IBM: Open source MINLP project (2012).
  4. 4.
    Corporation, I.: IBM ILOG CPLEX V12.6 User’s Manual for CPLEX (2015).
  5. 5.
    D’Ambrosio, C., Lodi, A.: Mixed integer nonlinear programming tools: a practical overview. 4OR 9(4), 329–349 (2011).
  6. 6.
    Duran, M., Grossmann, I.: An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Program. 36, 307–339 (1986). Scholar
  7. 7.
    Fletcher, R., Leyffer, S.: Solving mixed integer nonlinear programs by outer approximation. Math. Program. 66, 327–349 (1994). Scholar
  8. 8.
    Hemmecke, R., Köppe, M., Lee, J., Weismantel, R.: Nonlinear integer programming. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008, pp. 561–618. Springer, Heidelberg (2010).
  9. 9.
    Leyffer, S.: Macminlp: Test problems for mixed integer nonlinear programming (2003). (2013).
  10. 10.
    Melo, W., Fampa, M., Raupp, F.: Integrating nonlinear branch-and-bound and outer approximation for convex mixed integer nonlinear programming. J. Glob. Optim. 60(2), 373–389 (2014). Scholar
  11. 11.
    Melo, W., Fampa, M., Raupp, F.: Integrality gap minimization heuristics for binary mixed integer nonlinear programming. J. Glob. Optim. 71(3), 593–612 (2018).
  12. 12.
    Melo, W., Fampa, M., Raupp, F.: An overview of MINLP algorithms and their implementation in muriqui optimizer. Ann. Oper. Res. (2018).
  13. 13.
    Trespalacios, F., Grossmann, I.E.: Review of mixed-integer nonlinear and generalized disjunctive programming methods. Chem. Ing. Tech. 86(7), 991–1012 (2014). Scholar
  14. 14.
    Westerlund, T., Pettersson, F.: An extended cutting plane method for solving convex MINLP problems. Comput. Chem. Eng. 19(Supplement 1), 131–136 (1995). European Symposium on Computer Aided Process Engineering
  15. 15.
    World, G.: MINLP library 2 (2014).

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Authors and Affiliations

  1. 1.College of Computer ScienceFederal University of UberlandiaUberlândiaBrazil
  2. 2.Institute of Mathematics and COPPEFederal University of Rio de JaneiroJaneiroBrazil
  3. 3.National Laboratory for Scientific Computing (LNCC) of the Ministry of ScienceTechnology and InnovationPetrópolisBrazil

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