学术报告

Optimality Conditions and Numerical Algorithms for a Class of Linearly Constrained Minimax Optimization Problems

戴彧虹 研究员

（中国科学院数学与系统科学研究院）

报告时间: 2022年5月17日 星期三  14：00-15：00

报告地点: 沙河主楼E405

腾讯会议：861-172-286

报告摘要: It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality conditions and develop practical numerical algorithms for minimax problems with joint linear constraints. First of all, we use the properties of proximal mapping and KKT system to establish optimality conditions. Secondly, we propose a framework of alternating coordinate algorithm for the minimax problem and analyze its convergence properties. Thirdly, we develop a proximal gradient multi-step ascent decent method (PGmsAD) as a numerical algorithm and provide the iteration complexity result for the algorithm. Finally, we apply PGmsAD to generalized absolute value equations, generalized linear projection equations and linear regression problems and report the efficiency of PGmsAD on large-scale optimization. This is a joint wok with Jiani Wang and Liwei Zhang.

报告人简介：

戴彧虹研究员，博士生导师,中国科学院数学与系统研究院副院长, 中国运筹学会理事长，亚太运筹学会联合会主席。戴彧虹教授长期从事优化方法的理论及应用研究，在连续优化、整数规划和应用优化等方面作出了系统的创造性工作。曾或正主持国家杰出青年科学基金、国家基金委创新研究群体项目、“十四五”国家重点研发计划项目等多项基金项目。应邀在2022年国际数学家大会做45分钟邀请报告，在第24届国际数学规划大会作一小时邀请报告。 曾获国家自然科学二等奖、中国青年科技奖、钟家庆数学奖、冯康科学计算奖、陈省身数学奖和首届萧树铁应用数学奖等奖项。

邀请人：韩德仁