报告人：刘歆 研究员
报告题目：A Penalty-free Infeasible Approach for a Class of Nonsmooth Optimization Problems over the Stiefel Manifold
主持人：徐玮玮 教授
报告时间：2022年1月10日10:00-11:00
报告地点：腾讯会议（ID: 765-515-617）
欢迎广大师生聆听！
报告摘要：
Transforming into an exact penalty function model with convex compact constraints yields efficient infeasible approaches for optimization problems with orthogonality constraints. For smooth and ℓ2,1-norm regularized cases, these infeasible approaches adopt simple and orthonormalization-free updating scheme and show their high efficiency in the test examples. However, to avoid orthonormalization while enforcing the feasibility of the final solution, these infeasible approaches introduce a quadratic penalty term, where an inappropriate penalty parameter can lead to numerical inefficiency. Inspired by penalty-free approaches for smooth optimization problems, we proposed a proximal first-order algorithm for a class of optimization problems with orthogonality constraints and nonsmooth regularization term. The consequent algorithm, named sequential linearized proximal gradient method (SLPG), alternatively takes tangential steps and normal steps to improve the optimality and feasibility respectively. In SLPG, the orthonormalization process is invoked only once at the last step if high precision in feasibility is needed, showing that main iterations in SLPG are orthonormalization-free. Besides, both the tangential steps and normal steps do not involve the penalty parameter, and thus SLPG is penalty-free and avoids the inefficiency by inappropriate penalty parameter. We analyze the global convergence properties of SLPG where the tangential steps are inexactly computed. By inexactly computing tangential steps, for smooth cases and ℓ2,1-norm regularized cases, SLPG has a closed-form updating scheme, which leads to its cheap tangential steps. Numerical experiments illustrate the numerical advantages of SLPG when compared with existing first-order methods.
报告人简介：
刘歆，中国科学院数学与系统科学研究院，冯康首席研究员。
2004年本科毕业于北京大学数学科学学院；2009年于中国科学院数学与系统科学研究院获得博士学位；毕业后留所工作至今。曾在德国Zuse Institute Berlin，美国Rice大学，美国纽约大学Courant研究所等科研院所长期访问。主要研究方向包括：流形优化、分布式优化、统计大数据分析、材料计算、机器学习等。2016年获得国家优秀青年科学基金；2016年获得中国运筹学会青年科技奖；2020年获得中国工业与应用数学学会应用数学青年科技奖；2021年获得国家杰出青年科学基金。目前担任《Mathematical Programming Computation》、《Journal of Computational Mathematics》、《Journal of Industrial and Management Optimization》等国内外期刊编委；并担任中国运筹学会常务理事，中国工业与应用数学会副秘书长。
数学与统计学院
2022年1月5日
