报告题目：Generalizing Nesterov’s Scheme and Magical High-order Methods

报告时间：2023年4月10日（周一）13：30

报告地点：C1-437

主讲人：洪涛博士

报告摘要：With engineering and science being increasingly data driven, developing models with efficient algorithms to understand the information behind the data becomes the backbone of data science. First-order methods are widely used in many applications, e.g., linear and nonlinear inverse problems, signal processing, and machine learning, etc., because of its cheap computation at each iteration. But its efficiency remains a concern. Some accelerated methods have been developed that improve the efficiency of optimization and reach an optimal convergence rate. These accelerated methods are mainly based on Nesterov’s scheme. However, how to generalize Nesterov’s scheme to accelerate an abstract plain (without acceleration) iterative method is still unknown.

In the first part of the talk, I will introduce a way to generalize Nesterov’s scheme to accelerate abstract plain iterative methods for linear problems. High-order methods converge faster than first-order methods. But it is hard to use high-order methods for real applications because high-order methods require much higher computation than first-order methods at each iteration.

In the second part of the talk, I will discuss a specifical high-order method and derive a way to reduce the computation at each iteration. Finally, I will show the potential advantage of high-order methods for image reconstruction in compressive sensing MRI.

主讲人简介：洪涛，现任美国密西根大学电气工程与计算机科学学院和功能性核磁共振成像实验室博士后研究员。2012年获浙江工业大学通信工程学士，2021年获得以色列理工学院计算机科学博士。主要研究领域包括：优化理论与多重网格计算方法。他在设计高效计算方法领域做了许多工作，相关算法在科学计算，信号处理，机器学习及计算成像等领域得到了应用。近期，洪博士主要研究方向为核磁共振成像和光学衍射层析成像的计算方法，及高阶算法。