报告题目 (Title)：Global optimization algorithms for fractional programming problems （分式规划问题的全局优化算法）

报告人 (Speaker)：申培萍 教授（华北水利水电大学）

报告时间 (Time)：2024年5月29日 (周三) 10:00

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：徐姿 教授

主办部门：理学院数学系

报告摘要：Fractional programming problems have been widely studied due to their importance from both theoretical and practical perspectives. Theoretically, fractional programming problem has many locally optimal solutions which are not globally optimal. In practice, it has spawned a wide variety of applications in bond portfolio optimization, system reliability analysis, computer vision and so on. From the computational point of view, various approaches have been proposed to tackle it, such as outer approximation algorithm, branch and bound algorithm, approximation algorithm and so on. In this talk, we focus on two types of fractional programming problems: the sum of linear ratios programming problem and the minimax linear fractional programming problem. For sum of linear ratios problem, a spatial branch-and-bound algorithm is proposed by utilizing a second-order cone relaxation technique. This algorithm incorporates a region compression technique and an adaptive branching rule to enhance convergence. We also introduce a branch-and-bound algorithm based on the relaxation of a box-constrained two-layer problem. Additionally, the one-dimensional branching rule based branch-and-bound algorithm is considered for minimax linear fractional programming. Finally, the convergence and complexity of the developed algorithms are analyzed.