IDEAS home Printed from https://ideas.repec.org/a/wly/jjmath/v2025y2025i1n4452933.html

An Efficient Branch‐and‐Bound Algorithm for Globally Minimizing a Class of Generalized Linear Multiplicative Programs

Author

Listed:
  • Peng Hu
  • Zhiyou Wu
  • Tao Yang
  • Jia Liu
  • Bangying Xin

Abstract

This study presents a novel algorithm for globally solving generalized linear multiplicative programming (GLMP) problems. We first introduce a convex‐separation technique to craft a tight yet computationally tractable linear relaxation that supplies strong lower bounds for the original nonconvex formulation. Building upon this relaxation, a rigorous branch‐and‐bound framework is designed, and its global convergence is proved along with a comprehensive complexity analysis. Extensive numerical experiments demonstrate that the proposed algorithm significantly outperforms existing methods in both computational efficiency and robustness.

Suggested Citation

  • Peng Hu & Zhiyou Wu & Tao Yang & Jia Liu & Bangying Xin, 2025. "An Efficient Branch‐and‐Bound Algorithm for Globally Minimizing a Class of Generalized Linear Multiplicative Programs," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:4452933
    DOI: 10.1155/jom/4452933
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/jom/4452933
    Download Restriction: no
    File URL: https://libkey.io/10.1155/jom/4452933?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
    ---><---

    References listed on IDEAS

    as
    1. Chun-Feng Wang & San-Yang Liu & Geng-Zhong Zheng, 2011. "A Branch-and-Reduce Approach for Solving Generalized Linear Multiplicative Programming," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-12, July.
    2. Yuelin Gao & Siqiao Jin, 2013. "A Global Optimization Algorithm for Sum of Linear Ratios Problem," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, June.
    3. Mojtaba Borza & Azmin Sham Rambely, 2021. "A Linearization to the Sum of Linear Ratios Programming Problem," Mathematics, MDPI, vol. 9(9), pages 1-10, April.
    4. Yuelin Gao & Siqiao Jin, 2013. "A Global Optimization Algorithm for Sum of Linear Ratios Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    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. Hongwei Jiao & Yongqiang Chen, 2014. "A New Linearizing Method for Sum of Linear Ratios Problem with Coefficients," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Jiao, Hongwei & Ma, Junqiao, 2022. "An efficient algorithm and complexity result for solving the sum of general affine ratios problem," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Mojtaba Borza & Azmin Sham Rambely & Seyed Ahmad Edalatpanah, 2023. "A Linearization to the Multi-objective Linear Plus Linear Fractional Program," SN Operations Research Forum, Springer, vol. 4(4), pages 1-22, December.
    4. M. N. Yarahmadi & S. A. MirHassani & F. Hooshmand, 2023. "A heuristic method to find a quick feasible solution based on the ratio programming," Operational Research, Springer, vol. 23(3), pages 1-19, September.
    5. X. Liu & Y.L. Gao & B. Zhang & F.P. Tian, 2019. "A New Global Optimization Algorithm for a Class of Linear Fractional Programming," Mathematics, MDPI, vol. 7(9), pages 1-21, September.

    More about this item

    Statistics

    Access and download statistics

    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:wly:jjmath:v:2025:y:2025:i:1:n:4452933. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/1469 .

    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.