勷勤数学•专家报告

题      目：Riemannian ADMM for Three-Block Nonconvex Nonsmooth Composite Optimization

报  告  人： 唐春明 教授  (邀请人：陈艳男)

                                              广西大学

时      间： 9月20日  16：30-17:30

地     点：数科院东楼二楼会议室

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。主持国家自然科学基金面上项目、广西自然科学基金杰出青年基金、广西自然科学基金重点项目等课题8项。在Computational Optimization and Applications、Journal of Optimization Theory and Applications、European Journal of Operational Research、中国科学（数学）等刊物发表论文50余篇。

摘      要：

          The alternating direction method of multipliers (ADMM) is widely recognized as an efficient approach for composite optimization problems in Euclidean spaces. Although ADMM has recently been extended to the Riemannian setting, most existing variants are limited to two-block structures, thereby restricting their practical applicability and computational efficiency. This talk considers a class of nonconvex, nonsmooth, non-Lipschitz composite optimization problems on Riemannian manifolds, for which we develop a three-block Riemannian ADMM (TRADMM) by incorporating linearly coupled constraints into the reformulation. TRADMM employs computationally inexpensive closed-form updates in each iteration, thereby avoiding costly inner iterations and significantly reducing the total computational cost. The boundedness of the Lagrange multipliers is guaranteed through an adaptive update of the dual stepsize together with Moreau envelope smoothing. We analyze the iteration complexity of the proposed algorithm for finding an $\epsilon$-stationary point under mild assumptions. Numerical experiments on unsupervised feature selection show that the proposed method outperforms the compared methods in terms of computational efficiency.

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