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：Solving the Second-Order Cone Linear Complementarity Problem by the Lanczos Method
报告人： 丰博 博士 单位：扬州大学数学学院
报告时间：2026年9月19日（周六）上午 10:30-11:30
报告地点：数学学院A321
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数学学院
报告人及报告内容简介：
丰博，博士，扬州大学数学学院讲师。2024年博士毕业于中国矿业大学。主要研究领域为数值线性代数，大规模矩阵计算。主持国家自然科学青年基金项目1项，江苏省自然科学青年基金项目1项，中国博士后面上项目1项。在SIAM Journal on Scientific Computing, IMA Journal of Numerical Analysis, Applied Numerical Mathematics, Advances in Computational Mathematics, Numerical Linear Algebra with Applications等期刊发表学术论文多篇。
Abstract: For solving the large-scale (convex) second-order cone optimization problem (SOCLCP), we propose a block Lanczos method in this paper. By exploiting the structure of second-order cones and optimality conditions, we construct a suitable Krylov subspace as the search space, and the original large-scale problem is reduced to a small-sized one. Theoretical analysis demonstrates that the convergence rate of the new algorithm is comparable to that of the conjugate gradient method. Moreover, we develop an eigenvalue-based algorithm for SOCLCP. We prove that solving the SOCLCP is equivalent to seeking the eigenpair with the largest (or second largest) real part of the eigenvalue of a particular matrix pencil, and provide a detailed theoretical analysis. Numerical experiments on medium-sized dense and large-scale sparse matrices show that the proposed method is superior to the state-of-the-art approaches. The new method not only yields highly accurate approximate solutions, but is also much faster than those approaches in terms of CPU time on most numerical examples.