IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v488y2025ics0096300324005757.html
   My bibliography  Save this article

A Lagrange barrier approach for the minimum concave cost supply problem via a logarithmic descent direction algorithm

Author

Listed:
  • Yu, Yaolong
  • Wu, Zhengtian
  • Jiang, Baoping
  • Yan, Huaicheng
  • Lu, Yichen

Abstract

The minimisation of concave costs in the supply chain presents a challenging non-deterministic polynomial (NP) optimisation problem, widely applicable in industrial and management engineering. To approximate solutions to this problem, we propose a logarithmic descent direction algorithm (LDDA) that utilises the Lagrange logarithmic barrier function. As the barrier variable decreases from a high positive value to zero, the algorithm is capable of tracking the minimal track of the logarithmic barrier function, thereby obtaining top-quality solutions. The Lagrange function is utilised to handle linear equality constraints, whilst the logarithmic barrier function compels the solution towards the global or near-global optimum. Within this concave cost supply model, a logarithmic descent direction is constructed, and an iterative optimisation process for the algorithm is proposed. A corresponding Lyapunov function naturally emerges from this descent direction, thus ensuring convergence of the proposed algorithm. Numerical results demonstrate the effectiveness of the algorithm.

Suggested Citation

  • Yu, Yaolong & Wu, Zhengtian & Jiang, Baoping & Yan, Huaicheng & Lu, Yichen, 2025. "A Lagrange barrier approach for the minimum concave cost supply problem via a logarithmic descent direction algorithm," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    • Handle: RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005757
    DOI: 10.1016/j.amc.2024.129114
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324005757
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.129114?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.

    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:eee:apmaco:v:488:y:2025:i:c:s0096300324005757. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.