深圳大学四十周年校庆暨数学学科四十周年庆

荔园杰出学者第二十一期

讲座题目:Optimality Conditions and Numerical Algorithms for Constrained Minimax Optimization Problems

主讲人：戴彧虹 研究员（中国科学院数学与系统科学研究院）

讲座时间：2023年12月13日（周三）10:10-11:10

讲座地点：深圳大学校友广场校友广场303会议室

内容概述：It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint constraints are very rare. This paper aims to discuss optimality conditions and develop practical numerical algorithms for two calsses of minimax problems, i.e., minimax problems with joint constraints and minimax problems with least constraint violation. First of all, we use the properties of proximal mapping and KKT system to establish optimality conditions and develop a proximal gradient multi-step ascent decent method (PGmsAD) as a numerical algorithm. Furthermore, we demonstrate that the method can establish the same iterative complexity as unconstrained minimax optimization. Secondly, we introduce the definition of the local minimax point and investigate the solvability of the dual of the optimization problem with the least constraint violation. Moreover, we establish the optimality conditions and propose the augmented Lagrangian method for the convex minimax optimization with the least constraint violation, which has the linear convergence rate under an error bound condition.

主讲人简介：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。

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2023年12月11日