报告人：唐春明 教授
报告题目：A restricted memory quasi-Newton bundle method for nonsmooth optimization on Riemannian manifolds
报告时间：2026年4月30日（周四）上午10：00
报告地点：腾讯会议：206-419-892
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
唐春明，博士，教授，博士生导师。现任广西大学数学学院副院长，兼任广西运筹学会副理事长、广西数学教育分会副理事长、广西数学会常务理事。主要研究方向：最优化理论与方法及其应用，非光滑优化，流形上的优化等。主持国家基金项目面上项目，广西基金杰青项目、广西基金重点项目等。在《Journal of Optimization Theory and Applications》、《Computational Optimization and Applications》、《European Journal of Operational Research 》、《中国科学：数学》等刊物发表论文50余篇。
报告摘要：
In this talk, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz continuous function over a Riemannian manifold is proposed. The curvature information of the objective function is approximated by applying a Riemannian version of the quasi-Newton updating formulas. A Riemannian subgradient aggregation technique is proposed and used to significantly reduce the computations in the quadratic programming subproblem when calculating the candidate descent direction. Moreover, a Riemannian line-search procedure is proposed to generate the stepsizes, and the process is finitely terminated under the assumption of a newly proposed Riemannian semismoothness. Global convergence of the proposed method is established: if the serious iteration steps are finite, then the last serious iterate is stationary; otherwise, every accumulation point of the serious iteration sequence is stationary. In addition, a modified algorithm with limited-memory quasi-Newton updates is presented to further reduce the computational cost. Finally, numerical experiments demonstrate that (i) the quasi-Newton updates accelerate the convergence of the bundle method, (ii) the aggregation technique significantly reduces the computational cost for solving the quadratic programming subproblem, and (iii) the proposed methods outperform the compared state-of-the-art Riemannian optimization methods for locally Lipschitz continuous functions.
