题目一：Stochastic dual coordinate descent algorithms for l1-norm minimization
内容简介：Finding a solution to the linear system Ax = b with various minimization properties arises from many engineering and computer science applications, including compressed sensing, image processing, and machine learning. In the era of big data, the stochastic optimization algorithms become increasingly significant due to their scalability for problems of unprecedented size. This talk focuses on the problem of minimizing a strongly convex function subject to linear constraints. We consider the dual formulation of this problem and adopt the stochastic coordinate descent to solve it. The proposed algorithmic framework, called fast stochastic dual coordinate descent, utilizes sampling matrices sampled from user-defined distributions to extract gradient information. Moreover, it employs Polyak's heavy ball momentum acceleration with adaptive parameters learned through iterations, overcoming the limitation of the heavy ball momentum method that it requires prior knowledge of certain parameters, such as the singular values of a matrix. With these extensions, the framework is able to recover many well-known methods in the context, including the randomized sparse Kaczmarz method, the randomized regularized Kaczmarz method, the linearized Bregman iteration, and a variant of the conjugate gradient (CG) method. We prove that, with strongly admissible objective function, the proposed method converges linearly in expectation. Numerical experiments are provided to confirm our results. The arXiv link: https://arxiv.org/abs/2307.16702.
报告人：谢家新
报告人简介：北京航空航天大学数学科学学院副研究员, 硕士生导师, 中国运筹学会数学规划分会青年理事. 2012年和2017年于湖南大学数学学院分别获得学士和博士学位, 2017-2019年于中国科学院数学与系统科学研究院从事博士后研究, 合作导师许志强研究员. 研究兴趣为数据科学中的数学问题, 特别是压缩感知、随机优化算法和子集选择等问题. 主持北航青年拔尖计划和国家自然科学基金青年等项目。
题目二：Uniqueness and Estimation Performance for Noisy Phase Retrieval
内容简介：The Wirtinger Flow-based model and Amplitude Flow-based model are commonly used estimators for solving phase retrieval problem. In this talk, we investigate the uniqueness of solutions for these two estimators in the presence of noise. We demonstrate that, for any given measurements, there exist certain levels of noise that result in non-unique solutions. However, it is worth noting that the estimation error remains small for all solutions and can be bounded by the average noise per measurement, irrespective of the noise structure. Additionally, we provide lower bounds for the estimation error, which demonstrate the optimality of our results.
报告人：黄猛
报告人简介：北京航空航天大学数学科学学院副教授。2019年博士毕业于中科院数学与系统科学研究院，2019-2021年期间在香港科技大学从事博士后。研究方向为相位恢复、矩阵偏差及数据科学中的优化问题。目前在 Applied and Computational Harmonic Analysis、Mathematics of Computation、SIAM Journal on Imaging Sciences、Inverse Problems、IEEE Transactions on Information Theory、Journal of Fourier Analysis and Applications、Advances in Applied Mathematics 等国际权威期刊上发表论文多篇。主持国家自然科学基金1项。
时 间：2023年10月18日（周三）下午14：30 始
地 点：腾讯会议：653-604-872
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