学术报告报告主题: Solving polynomial variational inequality problems via Lagrange multiplier expressions and Moment-SOS relaxations
报 告 人：张敏副教授
报告时间：2026年 3月20日（星期五）下午15:00-16:00
报告地点：清清文理楼3A02
邀 请 人: 张威副教授、俞礼军副教授
欢迎广大师生前往！
数学学院
2026年3月15日
报告摘要：
This paper focuses on the development of numerical methods for solving variational inequality problems (VIPs) with involved mappings and feasible sets characterized by polynomial functions. We propose a numerical algorithm for computing solutions to polynomial VIPs based on Lagrange multiplier expressions and the Moment-SOS hierarchy of semidefinite relaxations. Building upon this algorithm, we also extend to finding more or even all solutions to polynomial VIPs. This algorithm can find solutions to polynomial VIPs or determine their nonexistence within a finite number of steps, under some general assumptions. Moreover, it is demonstrated that if the VIP is represented by generic polynomial functions, a finite number of Karush–Kuhn– Tucker (KKT) points exist, and all solutions to the polynomial VIP are KKT points. The paper establishes that in such cases, the method is guaranteed to terminate within a finite number of iterations, with an upper bound for the number of KKT points determined using intersection theory. Finally, even when algorithms lack finite convergence, the paper demonstrates asymptotic convergence under specific continuity assumptions. Numerical experiments are conducted to illustrate the efficiency of the proposed methods.
报告人介绍：
张敏，广州大学数学与信息科学学院，副教授。2016年毕业于天津大学，2016-2019年在澳大利亚科廷大学从事博士后研究，主要研究方向为最优化理论、方法及其应用。2019年获得中国科学院百人计划青年项目支持，在中科院新疆生态与地理研究所担任副研究员，2024年获得广州大学“百人计划青年杰出人才”，入职广州大学数学与信息科学学院。近五年开展的研究工作主要围绕优化技术与气候变化及水资源管理相关应用之间的交叉科学问题，部分研究成果发表在SIAM Journal on Optimization, Mathematical Programming,IEEE Transaction on Information Theory，Journal of Hydrology：Regional Study等期刊，主持国家自然科学基金青年项目、面上项目、省部级基金项目等7项。