報告人：韓德仁 教授
報告題目：Flexible operator splitting methods for solving absolute value equations
報告時間：2025年10月30日（周四）下午 16：30
報告地點：云龍校區6號樓304會議室
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
韓德仁，教授，博士生導師，北京航空航天大學數學科學學院院長。從事大規模優化、變分不等式問題及其應用研究工作，發表多篇學術論文。曾獲中國運籌學會青年科技獎，江蘇省科學技術獎等獎項;主持國家自然科學基金重點項目、杰出青年基金項目等多項項目。擔任中國運籌學會副理事長、算法軟件與應用分會理事長；《數值計算與計算機應用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》編委。
報告摘要：
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.