IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v181y2019i3d10.1007_s10957-019-01499-7.html
   My bibliography  Save this article

On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition

Author

Listed:
  • Zhou Wei

    (Yunnan University)

  • M. Montaz Ali

    (University of the Witwatersrand)

  • Liang Xu

    (University of Pittsburgh)

  • Bo Zeng

    (University of Pittsburgh)

  • Jen-Chih Yao

    (Zhejiang Normal University
    China Medical University)

Abstract

In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01499-7
    DOI: 10.1007/s10957-019-01499-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-019-01499-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-019-01499-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Omprakash K. Gupta & A. Ravindran, 1985. "Branch and Bound Experiments in Convex Nonlinear Integer Programming," Management Science, INFORMS, vol. 31(12), pages 1533-1546, December.
    2. J. N. Hooker, 2007. "Planning and Scheduling by Logic-Based Benders Decomposition," Operations Research, INFORMS, vol. 55(3), pages 588-602, June.
    3. 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.
    4. Xiang Li & Asgeir Tomasgard & Paul I. Barton, 2011. "Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 425-454, December.
    5. 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.
    6. Boukouvala, Fani & Misener, Ruth & Floudas, Christodoulos A., 2016. "Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO," European Journal of Operational Research, Elsevier, vol. 252(3), pages 701-727.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Andrew Allman & Qi Zhang, 2021. "Branch-and-price for a class of nonconvex mixed-integer nonlinear programs," Journal of Global Optimization, Springer, vol. 81(4), pages 861-880, December.
    2. 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.
    3. 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.
    4. David E. Bernal & Zedong Peng & Jan Kronqvist & Ignacio E. Grossmann, 2022. "Alternative regularizations for Outer-Approximation algorithms for convex MINLP," Journal of Global Optimization, Springer, vol. 84(4), pages 807-842, December.
    5. Meenarli Sharma & Prashant Palkar & Ashutosh Mahajan, 2022. "Linearization and parallelization schemes for convex mixed-integer nonlinear optimization," Computational Optimization and Applications, Springer, vol. 81(2), pages 423-478, March.
    6. Andreas Lundell & Jan Kronqvist, 2022. "Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT," Journal of Global Optimization, Springer, vol. 82(4), pages 863-896, April.
    7. Bei, Xiaoqiang & Zhu, Xiaoyan & Coit, David W., 2019. "A risk-averse stochastic program for integrated system design and preventive maintenance planning," European Journal of Operational Research, Elsevier, vol. 276(2), pages 536-548.
    8. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    9. Özgün Elçi & John Hooker, 2022. "Stochastic Planning and Scheduling with Logic-Based Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2428-2442, September.
    10. Nascimento, Paulo Jorge & Silva, Cristóvão & Antunes, Carlos Henggeler & Moniz, Samuel, 2024. "Optimal decomposition approach for solving large nesting and scheduling problems of additive manufacturing systems," European Journal of Operational Research, Elsevier, vol. 317(1), pages 92-110.
    11. Li, Xin & Pan, Yanchun & Jiang, Shiqiang & Huang, Qiang & Chen, Zhimin & Zhang, Mingxia & Zhang, Zuoyao, 2021. "Locate vaccination stations considering travel distance, operational cost, and work schedule," Omega, Elsevier, vol. 101(C).
    12. Marcia Fampa & Jon Lee & Wendel Melo, 2016. "A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in n-space," Computational Optimization and Applications, Springer, vol. 65(1), pages 47-71, September.
    13. Jianyuan Zhai & Fani Boukouvala, 2022. "Data-driven spatial branch-and-bound algorithms for box-constrained simulation-based optimization," Journal of Global Optimization, Springer, vol. 82(1), pages 21-50, January.
    14. Radu Baltean-Lugojan & Ruth Misener, 2018. "Piecewise parametric structure in the pooling problem: from sparse strongly-polynomial solutions to NP-hardness," Journal of Global Optimization, Springer, vol. 71(4), pages 655-690, August.
    15. Campos, Juan S. & Misener, Ruth & Parpas, Panos, 2019. "A multilevel analysis of the Lasserre hierarchy," European Journal of Operational Research, Elsevier, vol. 277(1), pages 32-41.
    16. Chan, Chi Kin & Fang, Fei & Langevin, André, 2018. "Single-vendor multi-buyer supply chain coordination with stochastic demand," International Journal of Production Economics, Elsevier, vol. 206(C), pages 110-133.
    17. Zheng, Xuyue & Wu, Guoce & Qiu, Yuwei & Zhan, Xiangyan & Shah, Nilay & Li, Ning & Zhao, Yingru, 2018. "A MINLP multi-objective optimization model for operational planning of a case study CCHP system in urban China," Applied Energy, Elsevier, vol. 210(C), pages 1126-1140.
    18. Tony T. Tran & Arthur Araujo & J. Christopher Beck, 2016. "Decomposition Methods for the Parallel Machine Scheduling Problem with Setups," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 83-95, February.
    19. Fan-Yun Meng & Li-Ping Pang & Jian Lv & Jin-He Wang, 2017. "An approximate bundle method for solving nonsmooth equilibrium problems," Journal of Global Optimization, Springer, vol. 68(3), pages 537-562, July.
    20. Roshanaei, Vahid & Booth, Kyle E.C. & Aleman, Dionne M. & Urbach, David R. & Beck, J. Christopher, 2020. "Branch-and-check methods for multi-level operating room planning and scheduling," International Journal of Production Economics, Elsevier, vol. 220(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01499-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.