報(bào)告人：韓德仁 教授

報(bào)告題目：Flexible operator splitting methods for solving absolute value equations

報(bào)告時(shí)間：2025年10月30日（周四）下午 16：30

報(bào)告地點(diǎn)：云龍校區(qū)6號(hào)樓304會(huì)議室

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

韓德仁，教授，博士生導(dǎo)師，北京航空航天大學(xué)數(shù)學(xué)科學(xué)學(xué)院院長。從事大規(guī)模優(yōu)化、變分不等式問題及其應(yīng)用研究工作，發(fā)表多篇學(xué)術(shù)論文。曾獲中國運(yùn)籌學(xué)會(huì)青年科技獎(jiǎng)，江蘇省科學(xué)技術(shù)獎(jiǎng)等獎(jiǎng)項(xiàng);主持國家自然科學(xué)基金重點(diǎn)項(xiàng)目、杰出青年基金項(xiàng)目等多項(xiàng)項(xiàng)目。擔(dān)任中國運(yùn)籌學(xué)會(huì)副理事長、算法軟件與應(yīng)用分會(huì)理事長；《數(shù)值計(jì)算與計(jì)算機(jī)應(yīng)用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》編委。

報(bào)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.