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

Yaolong Yu, Zhengtian Wu, Baoping Jiang, Huaicheng Yan and Yichen Lu

Applied Mathematics and Computation, 2025, vol. 488, issue C

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.

Keywords: Concave cost supply problem; Combinatorial optimisation; A logarithmic descent direction algorithm; Lagrange logarithmic barrier function (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005757

DOI: 10.1016/j.amc.2024.129114

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