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

Peng Hu, Zhiyou Wu, Tao Yang, Jia Liu and Bangying Xin

Journal of Mathematics, 2025, vol. 2025, 1-19

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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:4452933

DOI: 10.1155/jom/4452933

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