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Inexact solution of NLP subproblems in MINLP

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  • M. Li
  • L. Vicente

Abstract

In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness in the limit case. Some numerical results will be presented to illustrate the behavior of the methods under NLP subproblem inexactness. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • M. Li & L. Vicente, 2013. "Inexact solution of NLP subproblems in MINLP," Journal of Global Optimization, Springer, vol. 55(4), pages 877-899, April.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:4:p:877-899
    DOI: 10.1007/s10898-012-0010-5
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    References listed on IDEAS

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    1. Pierre Bonami & João Gonçalves, 2012. "Heuristics for convex mixed integer nonlinear programs," Computational Optimization and Applications, Springer, vol. 51(2), pages 729-747, March.
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    Cited by:

    1. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Outer Approximation for Mixed-Integer Nonlinear Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1056-1086, December.

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