报告题目：On the quadratic termination property of the gradient method

报 告 人：黄亚魁 （准聘）教授 河北工业大学

邀请人：赵志华

报告时间：2023年5月30日（周二）14:30-16:50

报告地点：南校区网安大楼会议中心104会议室

报告人简介：黄亚魁，河北工业大学（准聘）教授，2015年博士毕业于bevictor伟德官网（导师：刘红卫教授），2015年7月至2017年5月在中国科学院数学与系统科学研究院从事博士后研究（合作导师：戴彧虹研究员），曾在美国路易斯安那州立大学访问一年（合作导师：张洪超教授）。主要研究兴趣包括梯度类算法理论及应用、大规模机器学习和分布式优化等领域的一阶算法，相关成果发表在SIAM Journal on Optimization、Journal of Scientific Computing、Computational Optimization and Applications等期刊，主持国家自然科学基金、河北省自然科学基金和中国博士后基金等科研项目。现任中国运筹学会数学规划分会理事、河北省运筹学会理事。

报告摘要：Due to its simplicity and efficiency, the gradient method has attracted more and more attentions in recent years. It is known that efficient optimization methods such as conjugate gradient method, quasi-Newton method and Newton method, enjoy the quadratic termination property. However, most existing gradient methods do not have such an attractive property. In this talk, we shall provide a summary account of three schemes to equip gradient methods with the two-dimensional quadratic termination property. Then we introduce a strategy for the gradient method to achieve three-dimensional quadratic termination. By incorporating the strategy with the steepest descent, minimal gradient and Barzilai-Borwein methods, we get four gradient methods. Some numerical results are reported to show that gradient methods can be significantly improved by equipping the three-dimensional quadratic termination property.