Series of Academic Reports of Jiangsu Applied Mathematics (China University of Mining and Technology) Center

Report Title: Numerical methods for symmetric and positive definite second-order cone linear complementarity problem

Presenter: Professor Wang Xiang, School of Mathematics and Computer Science, Nanchang University

Report time: 10:00-11:00 a.m. on Thursday, May 29, 2025

Report Location: Room A321, School of Mathematics

Biography of the Speaker: Wang Xiang, Ph.D., professor, and doctoral supervisor, is the vice dean of the School of Mathematics and Computer Science at Nanchang University, and the head of the first-level discipline doctoral program in mathematics and the postdoctoral research station in mathematics at Nanchang University. He/She has been successively selected or approved as a candidate of Jiangxi Province's New Century "Hundred, Thousand and Ten Thousand Talents Project", a candidate for Jiangxi Province's Young Scientist Program, a middle-aged and young backbone teacher in Jiangxi Province's Higher education institutions, and a recipient of Baosteel's National Excellent Teacher Award. Serves as a council member of the China Society for Industrial and Applied Mathematics, a council member of the Computational Mathematics Branch of the Chinese Mathematical Society, and an Associate Editor of the internationally renowned journal "Computational and Applied Mathematics". Mainly engaged in research in the fields of numerical algebra, artificial intelligence and data science, and has achieved some results in large-scale sparse linear equations, large-scale sparse eigenvalue problems, numerical solutions of linear and nonlinear matrix equations, spectral clustering, etc. At present, I am in charge of (including completed) 4 projects funded by the National Natural Science Foundation of China and over ten provincial and ministerial-level projects. in recent years, as the first author or corresponding author in Advance in Computational Mathematics, Journal of Scientific Computing Numerical Linear Algebra with Applications, Communications in Computational Physics and other international authoritative source journals by SCI journals published a total of more than 60 papers. As the first contributor, I have won one third prize of the Natural Science Award of Jiangxi Province and three second prizes of the Teaching Achievement Award of Jiangxi Province.

Report Summary: 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.