題目：納什議價問題中線性乘積規劃模型的分支定界算法（Branch and bound algorithms for linear multiplicative program in Nash bargaining problems）

演講人：申培萍教授🙍🏻‍♂️，華北水利水電大學

主持人：林貴華教授，意昂2

時間：2024年5月29日（周三），下午3:30

地點👨🏿‍🚀：意昂2注册校本部東區1號樓意昂2官网420會議室

主辦單位🌸：意昂2、意昂2青年教師聯誼會

演講人簡介👎：

國內著名運籌學專家🌟，華北水利水電大學二級教授👇🏿、博士生導師,河南省“傑青”，河南省“高層次人才”，河南省教育廳學術技術帶頭人，河南省教育系統優秀教師😰。

曾任中國運籌學會理事★，現任中國運籌學會數學規劃分會資深理事,河南省運籌學會副理事長,河南省數字圖形圖像學會常務理事🗡。

承擔國家自然科學基金7項💒，其中主持面上項目4項🩸，作為第一參與人2項。曾獲河南省傑出青年基金、河南省高校科技創新人才支持計劃等多項課題。

主要從事全局最優化理論、算法及其在工程領域中的應用研究。發表學術論文70余篇,獨著學術著作《全局優化方法》在科學出版社出版,獲河南省科技進步獎，以及河南省教學成果獎等多個獎項。

演講內容簡介👲🏻：

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.

歡迎廣大師生參加！