IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v86y2023i1d10.1007_s10898-022-01254-9.html
   My bibliography  Save this article

Nonconvex sensitivity-based generalized Benders decomposition

Author

Listed:
  • Jia-Jiang Lin

    (China University of Petroleum Beijing)

  • Feng Xu

    (China University of Petroleum Beijing)

  • Xiong-Lin Luo

    (China University of Petroleum Beijing)

Abstract

This paper considers general separable pseudoconvex optimization problems with continuous complicating variables in which primal and projected problems are both pseudoconvex problems. A novel decomposition method based on generalized Benders decomposition, named nonconvex sensitivity-based generalized Benders decomposition, is developed and proved strictly to obtain optimal solutions of general separable pseudoconvex optimization problems of interest without constructing surrogate models. By the use of a reformulation strategy (introducing an extra equality constraint and constructing several subproblems), the algorithm handles the nonconvexity by direct manipulations of consistent linear Benders cuts and the check of optimality conditions and approximating the feasible region of complicating variables by supporting hyperplanes. The master problems of the new algorithm are always linear programming problems and the solution of the algorithm contains sensitivity information about complicating variables. Moreover, the new algorithm could also be used as a tool to check the nonconvexity of an optimization problem. Two cases are given to confirm the validity and applicability of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:1:d:10.1007_s10898-022-01254-9
    DOI: 10.1007/s10898-022-01254-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01254-9
    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/s10898-022-01254-9?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. Can Li & Ignacio E. Grossmann, 2019. "A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables," Journal of Global Optimization, Springer, vol. 75(2), pages 247-272, October.
    2. Emmanuel Ogbe & Xiang Li, 2019. "A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs," Journal of Global Optimization, Springer, vol. 75(3), pages 595-629, November.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    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. Can Li & Ignacio E. Grossmann, 2019. "A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables," Journal of Global Optimization, Springer, vol. 75(2), pages 247-272, October.
    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.
    4. 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.
    5. 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.
    6. Kuttner, Leopold, 2022. "Integrated scheduling and bidding of power and reserve of energy resource aggregators with storage plants," Applied Energy, Elsevier, vol. 321(C).
    7. 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.
    8. Subramanian, Avinash S.R. & Gundersen, Truls & Barton, Paul I. & Adams, Thomas A., 2022. "Global optimization of a hybrid waste tire and natural gas feedstock polygeneration system," Energy, Elsevier, vol. 250(C).
    9. Can Li & Ignacio E. Grossmann, 2019. "A finite $$\epsilon $$ϵ-convergence algorithm for two-stage stochastic convex nonlinear programs with mixed-binary first and second-stage variables," Journal of Global Optimization, Springer, vol. 75(4), pages 921-947, December.
    10. Hesamzadeh, M. & Holmberg, P. & Sarfati, M., 2018. "Simulation and Evaluation of Zonal Electricity Market Designs," Cambridge Working Papers in Economics 1829, Faculty of Economics, University of Cambridge.
    11. Emmanuel Ogbe & Xiang Li, 2019. "A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs," Journal of Global Optimization, Springer, vol. 75(3), pages 595-629, November.
    12. Tapia-Ubeda, Francisco J. & Miranda, Pablo A. & Macchi, Marco, 2018. "A Generalized Benders Decomposition based algorithm for an inventory location problem with stochastic inventory capacity constraints," European Journal of Operational Research, Elsevier, vol. 267(3), pages 806-817.
    13. Yankai Cao & Victor M. Zavala, 2019. "A scalable global optimization algorithm for stochastic nonlinear programs," Journal of Global Optimization, Springer, vol. 75(2), pages 393-416, October.
    14. Steffen Rebennack, 2016. "Computing tight bounds via piecewise linear functions through the example of circle cutting problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 3-57, August.
    15. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    16. Tiago Andrade & Nikita Belyak & Andrew Eberhard & Silvio Hamacher & Fabricio Oliveira, 2022. "The p-Lagrangian relaxation for separable nonconvex MIQCQP problems," Journal of Global Optimization, Springer, vol. 84(1), pages 43-76, September.
    17. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    18. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    19. Yin, Yue & Liu, Tianqi & Wu, Lei & He, Chuan & Liu, Yikui, 2021. "Frequency-constrained multi-source power system scheduling against N-1 contingency and renewable uncertainty," Energy, Elsevier, vol. 216(C).
    20. Kamil A. Khan & Harry A. J. Watson & Paul I. Barton, 2017. "Differentiable McCormick relaxations," Journal of Global Optimization, Springer, vol. 67(4), pages 687-729, April.

    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:jglopt:v:86:y:2023:i:1:d:10.1007_s10898-022-01254-9. 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.