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

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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, Hindawi, vol. 2025, pages 1-19, October.
    • Handle: RePEc:hin:jjmath:4452933
    DOI: 10.1155/jom/4452933
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