【01.13 8#108】Alternating Direction Method of Multipliers for Robust Low Rank Matrix Completion

报告题目:Alternating Direction Method of Multipliers for Robust Low Rank Matrix Completion 



报告时间: 2020年1月13日14:40-15:20


报告摘要: In this paper, we propose a novel robust low rank matrix completion model, which adds the -norm penalty to the rank function in the objective function in order to alleviate the row structured noise. The first-order necessary optimality condition of the new model is given. We adapt the alternating direction method of multipliers (ADMM) to solve the nonconvex non-Lipschitz and discontinuous model directly and show its convergence under certain assumptions. Finally, extensive numerical results on artificial and real datasets show that the ADMM can efficiently solve our model, and provide the results that own the low rank structure of the matrix and the accuracy better than the state-of-the-art methods.

报告人简介:张超,北京交通大学理学院教授,博士生导师,研究方向为随机规划、矩阵优化等最优化理论、方法及应用。主持、参与了高维约束最小二乘问题的快速稳健算法设计及应用、图像恢复与分类的优化模型和算法研究、先验统计模型的建立与非线性优化理论等国家自然基金面上、科技部“973”重点项目研究。文章多次发表在Mathematical Programming、SIAM Journal on Optimization、Transportation Research Part B-Methodological、IEEE Transactions on Image Processing、SIAM Journal on Scientific Computing等顶级期刊。主要学术贡献包括:(一)较早地探讨了随机互补问题的期望残差最小(ERM)模型;(二)提出光滑投影梯度方法求解ERM模型,并将其推广到求解目标函数非Lipschitz的非光滑优化问题中;(三)将期望残差最小模型、光滑化算法及矩阵优化算法应用到交通、图像恢复等领域。