報告人：唐春明 教授
報告題目：A restricted memory quasi-Newton bundle method for nonsmooth optimization on Riemannian manifolds
報告時間：2026年4月30日（周四）上午10：00
報告地點：騰訊會議：206-419-892
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
唐春明，博士，教授，博士生導師?，F任廣西大學數學學院副院長，兼任廣西運籌學會副理事長、廣西數學教育分會副理事長、廣西數學會常務理事。主要研究方向：最優化理論與方法及其應用，非光滑優化，流形上的優化等。主持國家基金項目面上項目，廣西基金杰青項目、廣西基金重點項目等。在《Journal of Optimization Theory and Applications》、《Computational Optimization and Applications》、《European Journal of Operational Research 》、《中國科學：數學》等刊物發表論文50余篇。
報告摘要：
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.