江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：Numerical methods for symmetric and positive definite second-order cone linear complementarity problem
报告人：汪祥教授南昌大学数学与计算机学院
报告时间：2025年5月29日（周四）上午 10：00-11：00
报告地点：数学学院 A321
报告人简介：汪祥，博士、教授、博士生导师，南昌大学数学与计算机学院副院长、南昌大学数学一级学科博士学位点和数学博士后流动站负责人。先后入选或获批江西省新世纪百千万人才工程人选，江西省青年科学家人选，江西省高等学校中青年骨干教师，宝钢全国优秀教师奖获得者；担任中国工业与应用数学学会理事，中国数学会计算数学分会理事, 国际知名期刊《Computational and Applied Mathematics》的Associate Editor。 主要从事数值代数、人工智能与数据科学等领域的研究，在大规模稀疏线性方程组、大规模稀疏特征值问题、线性和非线性矩阵方程的数值求解、谱聚类等方面取得了一些成果。目前主持(含完成)国家自然科学基金4项及省部级项目十几项。近几年以第一作者或通讯作者在Advance in Computational Mathematics, Journal of Scientific Computing, Numerical Linear Algebra with Applications,Communications in Computational Physics等国际权威期刊上共发表SCI收录论文60多篇。以第一完成人身份获江西省自然科学奖三等奖1项和江西省教学成果奖二等奖3项。
报告摘要：The second-order cone linear complementarity problem (SOCLCP) is a generalization of the classical linear complementarity problem. It has been known that SOCLCP, with the globally uniquely solvable property, can be solved by convert equivalently to a zero-finding problem in which the associated function bears much similarity to the transfer function in model reduction. In this talk, we propose a new rational Krylov subspace method to solve the zero-finding problem for the symmetric and positive definite SOCLCP. The algorithm consists of two stages: first, it relies on an extended Krylov subspace to obtain an approximation of the zero root, and then applies multiple-pole rational Krylov subspace projections iteratively to acquire an accurate solution. Numerical evaluations on various types of SOCLCP examples demonstrate its efficiency and robustness.