Branch and bound algorithms for linear multiplicative program in Nash bargaining problems

报告题目：Branch and bound algorithms for linear multiplicative program in Nash bargaining problems

报告人：申培萍,华北水利水电大学，二级教授

报告时间：2024年5月28日下午 15：00-16：00

报告地点：上海财经大学红瓦楼826

报告摘要：The bargaining problem is a cooperative game in which all participants agree to form a coalition, instead of competing with each other, to get a higher payoff. Therefore, a key issue to address is determining the payoff for each participant in this coalition. The Nash bargaining solution indicates that for two participants, the problem of maximizing the payoff for each player can be modeled as the linear multiplicative programming problem (LMP). This highlights the importance of establishing efficient algorithms for solving (LMP). In this talk, we focus on developing various branch and bound methods for (LMP). To this end, a new bounding technique is proposed by integrating two linear relaxation methods, then a linear relaxation branch and bound algorithm is presented. Also, we establish a novel second order cone relaxation for (LMP), thus the process of solving (LMP) can be translated into solving a series of second order cone programs. Additionally, a simplicial branch and bound algorithm is designed to solve (LMP) based on a new convex quadratic relaxation and simplicial branching process. Finally, we analyze the convergence and complexity of the developed algorithms, and numerical results demonstrate their efficiency.

报告人简介：申培萍,华北水利水电大学，二级教授，博士生导师, 河南省管高校“高层次人才”，河南省教育厅学术技术带头人，河南省教育系统优秀教师。曾任中国运筹学会理事。现任中国运筹学会数学规划分会资深理事, 河南省运筹学会副理事长, 河南省数字图形图像学会常务理事。 主要从事全局最优化理论、算法及其在工程领域中的应用研究。承担国家自然科学基金项目7项，其中主持面上项目4项，作为第一参与人2项。曾获河南省杰出青年基金、河南省高校科技创新人才支持计划等多项研究课题。发表学术论文70余篇,独著学术著作《全局优化方法》在科学出版社出版,获河南省科技进步奖，以及河南省教学成果奖等多个奖项。

报告邀请人：王燕军 教授