报告地点：行健楼学术活动室526
邀请人：姜波教授
Abstract:
Recently, there has been growing interest in minimax problems on Riemannian manifolds due to their wide applications in machine learning and signal processing. Although many algorithms have been developed for minimax problems in the Euclidean setting, relatively few works studied minimax problems on manifolds. In this talk, we focus on the nonconvex-linear minimax problem on Riemannian manifolds. We propose a flexible Riemannian alternating descent ascent (RADA) algorithmic framework and prove that it achieves the best-known iteration complexity known to date. Various customized simple yet efficient algorithms can be incorporated within the proposed algorithmic framework and applied to different problem scenarios. We also reveal intriguing connections between the algorithms developed within our proposed framework and existing algorithms, which provide important insights into why the former outperform the latter. Lastly, we report extensive numerical results on sparse principal component analysis (PCA), fair PCA, and sparse spectral clustering to demonstrate the superior performance of the proposed algorithms.
Short bio: 刘亚锋，现为中国科学院数学与系统科学研究院副研究员。主要研究兴趣是最优化理论与算法及其在信号处理、无线通信和机器学习等领域中的应用。曾获2011年国际通信大会“最佳论文奖”，2018年数学与系统科学研究院“陈景润未来之星”，2018年中国运筹学会“青年科技奖”，2020年IEEE通信学会亚太地区“杰出青年学者奖”，2022年中国工业与应用数学学会“青年科技奖”等。他目前或曾担任《IEEE Transactions on Signal Processing》、《IEEE Transactions on Wireless Communications》、《IEEE Signal Processing Letters》、《Journal of Global Optimization》和《计算数学》期刊的编委以及《IEEE Journal on Selected Areas in Communications》期刊“无线通信网络中的优化理论与算法”专刊的客座编委。他是IEEE信号处理学会SPCOM（Signal Processing for Communications and Networking）的技术委员会成员。他的工作获得国家自然科学基金委青年基金、面上项目和优秀青年基金的资助。
