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Outer Approximation Algorithm for One Class of Convex Mixed-Integer Nonlinear Programming Problems with Partial Differentiability

Author

Listed:
  • Zhou Wei

    (Yunnan University
    University of the Witwatersrand, Wits)

  • M. Montaz Ali

    (University of the Witwatersrand, Wits)

Abstract

In this paper, we mainly study one convex mixed-integer nonlinear programming problem with partial differentiability and establish one outer approximation algorithm for solving this problem. With the help of subgradients, we use the outer approximation method to reformulate this convex problem as one equivalent mixed-integer linear program and construct an algorithm for finding optimal solutions. The result on finite steps convergence of the algorithm is also presented.

Suggested Citation

  • Zhou Wei & M. Montaz Ali, 2015. "Outer Approximation Algorithm for One Class of Convex Mixed-Integer Nonlinear Programming Problems with Partial Differentiability," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 644-652, November.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0715-y
    DOI: 10.1007/s10957-015-0715-y
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    Cited by:

    1. Jia-Jiang Lin & Feng Xu & Xiong-Lin Luo, 2023. "Nonconvex sensitivity-based generalized Benders decomposition," Journal of Global Optimization, Springer, vol. 86(1), pages 37-60, May.
    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.
    3. 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.

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