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LaGO: a (heuristic) Branch and Cut algorithm for nonconvex MINLPs


  • Ivo Nowak
  • Stefan Vigerske



We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integer nonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not require an algebraic representation of the problem, reformulation techniques for the construction of the convex relaxation cannot be applied, and we are restricted to sampling techniques in case of nonquadratic nonconvex functions. The linear relaxation is further improved by mixed-integer-rounding cuts. Also box reduction techniques are applied to improve efficiency. Numerical results on medium size test problems are presented to show the efficiency of the method. Copyright Springer-Verlag 2008

Suggested Citation

  • Ivo Nowak & Stefan Vigerske, 2008. "LaGO: a (heuristic) Branch and Cut algorithm for nonconvex MINLPs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 127-138, June.
  • Handle: RePEc:spr:cejnor:v:16:y:2008:i:2:p:127-138
    DOI: 10.1007/s10100-007-0051-x

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    Cited by:

    1. repec:spr:jglopt:v:67:y:2017:i:4:d:10.1007_s10898-016-0450-4 is not listed on IDEAS
    2. Zhou Wei & M. Ali, 2015. "Convex mixed integer nonlinear programming problems and an outer approximation algorithm," Journal of Global Optimization, Springer, vol. 63(2), pages 213-227, October.


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