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Two linear approximation algorithms for convex mixed integer nonlinear programming

Author

Listed:
  • Wendel Melo

    (Federal University of Uberlandia)

  • Marcia Fampa

    (Federal University of Rio de Janeiro)

  • Fernanda Raupp

    (National Laboratory for Scientific Computing of the Ministry of Science, Technology, Innovations and Communications)

Abstract

We present two new algorithms for convex Mixed Integer Nonlinear Programming (MINLP), both based on the well known Extended Cutting Plane (ECP) algorithm proposed by Weterlund and Petersson. Our first algorithm, Refined Extended Cutting Plane (RECP), incorporates additional cuts to the MILP relaxation of the original problem, obtained by solving linear relaxations of NLP problems considered in the Outer Approximation algorithm. Our second algorithm, Linear Programming based Branch-and-Bound (LP-BB), applies the strategy of generating cuts that is used in RECP, to the linear approximation scheme used by the LP/NLP based Branch-and-Bound algorithm. Our computational results show that RECP and LP-BB are highly competitive with the most popular MINLP algorithms from the literature, while keeping the nice and desirable characteristic of ECP, of being a first-order method.

Suggested Citation

  • Wendel Melo & Marcia Fampa & Fernanda Raupp, 2022. "Two linear approximation algorithms for convex mixed integer nonlinear programming," Annals of Operations Research, Springer, vol. 316(2), pages 1471-1491, September.
    • Handle: RePEc:spr:annopr:v:316:y:2022:i:2:d:10.1007_s10479-020-03722-5
    DOI: 10.1007/s10479-020-03722-5
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    References listed on IDEAS

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    1. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2018. "Integrality gap minimization heuristics for binary mixed integer nonlinear programming," Journal of Global Optimization, Springer, vol. 71(3), pages 593-612, July.
    2. Wendel Melo & Marcia Fampa & Fernanda Raupp, 2014. "Integrating nonlinear branch-and-bound and outer approximation for convex Mixed Integer Nonlinear Programming," Journal of Global Optimization, Springer, vol. 60(2), pages 373-389, October.
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