題目一：Stochastic dual coordinate descent algorithms for l1-norm minimization
内容簡介：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.
報告人：謝家新
報告人簡介：北京航空航天大學數學科學學院副研究員, 碩士生導師, 中國運籌學會數學規劃分會青年理事. 2012年和2017年于湖南大學數學學院分别獲得學士和博士學位, 2017-2019年于中國科學院數學與系統科學研究院從事博士後研究, 合作導師許志強研究員. 研究興趣為數據科學中的數學問題, 特别是壓縮感知、随機優化算法和子集選擇等問題. 主持北航青年拔尖計劃和國家自然科學基金青年等項目。
題目二：Uniqueness and Estimation Performance for Noisy Phase Retrieval
内容簡介：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.
報告人：黃猛
報告人簡介：北京航空航天大學數學科學學院副教授。2019年博士畢業于中科院數學與系統科學研究院，2019-2021年期間在香港科技大學從事博士後。研究方向為相位恢複、矩陣偏差及數據科學中的優化問題。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 等國際權威期刊上發表論文多篇。主持國家自然科學基金1項。
時 間：2023年10月18日（周三）下午14：30 始
地 點：騰訊會議：653-604-872
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