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

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.