上海管理论坛第523期

题目：纳什议价问题中线性乘积规划模型的分支定界算法（Branch and bound algorithms for linear multiplicative program in Nash bargaining problems）

演讲人：申培萍教授，华北水利水电大学

主持人：林贵华教授，8188威尼斯娱人城管理学院

时间：2024年5月29日（周三），下午3:30

地点：8188威尼斯娱人城校本部东区1号楼管理学院420会议室

主办单位：8188威尼斯娱人城管理学院、8188威尼斯娱人城管理学院青年教师联谊会

演讲人简介：

国内著名运筹学专家，华北水利水电大学二级教授、博士生导师,河南省“杰青”，河南省“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。

承担国家自然科学基金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课题。

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。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。

演讲内容简介：

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.

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