<p>This paper proposes a convex relaxation-based output space branch-reduction-bound algorithm for solving generalized fractional multiplicative programs (GLFMP). First, reciprocal variables are introduced to derive an equivalent problem (EP) for GLFMP. Second, the constraints of the equivalently reformulated EP are relaxed convexly to obtain a nonlinear relaxation problem, and then two equivalent convex programming formulations for it are constructed, leading to two convex relaxation problems for EP. Third, to enhance the efficiency of the algorithm, an output space region reduction technique is designed based on the analytical structure of the EP. Thus, two global optimization algorithms are proposed, and their convergence and complexity are analyzed. Finally, numerical experiments demonstrate that two proposed algorithms are feasible and effective.</p>