报告人：韩德仁 教授
报告题目：Flexible operator splitting methods for solving absolute value equations
报告时间：2025年10月30日（周四）下午 16：30
报告地点：云龙校区6号楼304会议室
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
韩德仁，教授，博士生导师，北京航空航天大学数学科学学院院长。从事大规模优化、变分不等式问题及其应用研究工作，发表多篇学术论文。曾获中国运筹学会青年科技奖，江苏省科学技术奖等奖项;主持国家自然科学基金重点项目、杰出青年基金项目等多项项目。担任中国运筹学会副理事长、算法软件与应用分会理事长；《数值计算与计算机应用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》编委。
报告摘要：
The operator splitting methods exhibit excellent ability in solving large-scale absolute equations, especially the inexact versions. However, two important parameters which play a crucial role in numerical performance are not judiciously addressed. One is the parameter in the residual which is fixed as a constant. The other one is the error tolerance parameter in the inaccuracy criterion which is hard to determine since it involves the estimation of an error-bound constant. By using a different potential function in convergence analysis, we design two new error criteria whose parameters do not rely on any estimation of other parameters. The algorithms are flexible in the sense that the accuracy criterion is a relative one and the parameter is an arbitrary one. Our methods avoid the task of presetting a sequence of parameters in the absolute error accuracy criterion and estimation of an upper bound involving the inputting data in other relative accuracy criteria. We report some promising numerical results.
