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Convex mixed integer nonlinear programming problems and an outer approximation algorithm

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  • Zhou Wei
  • M. Ali

Abstract

In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:2:p:213-227
    DOI: 10.1007/s10898-015-0284-5
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Zhou Wei & M. Montaz Ali & Liang Xu & Bo Zeng & Jen-Chih Yao, 2019. "On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 840-863, June.
    2. Felipe Serrano & Robert Schwarz & Ambros Gleixner, 2020. "On the relation between the extended supporting hyperplane algorithm and Kelley’s cutting plane algorithm," Journal of Global Optimization, Springer, vol. 78(1), pages 161-179, September.

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