走向现代数学学术报告 - 白正简教授（No. 715）

题目：Scaled Proximal Gradient Methods for Sparse Optimization Problems

报告人：白正简 教授（厦门大学）

时 间：2024年5月27日 9:00

地 点：东海岸校区-E414

摘要：Thresholding-based methods are widely used for sparse optimization problems in many applications including compressive sensing, image processing, and machine learning. However, the hard thresholding method may converge slowly or diverge for many practical problems. In this talk, we introduce a scaled proximal gradient method for solving sparse optimization problems, where the scaled matrix can take a varying positive diagonal for connecting the residual reduction. The global convergence of the proposed method is established under some mild assumptions. We also present a scaled proximal pursuit and a modified scaled proximal gradient method with global convergence under the restricted isometry property. Finally, some numerical tests are reported to illustrate the efficiency of the proposed methods over the classical thresholding-based methods.

报告人简介：白正简，厦门大学教授、博士生导师，福建省杰出青年基金获得者。2004年博士毕业于香港中文大学，曾在新加坡国立大学和意大利Insubria 大学作博士后和访问学者。主要研究方向为数值代数、特征值问题及其逆问题、稀疏优化、矩阵流形上的优化算法及其在数据科学中的应用等。主持国家自然科学基金面上项目和福建省自然科学基金项目多项。在SIAM J. Matrix Anal. Appl., SIAM J. Numer. Anal., Numer. Math., Inverse Problems, J. Sci. Comput. 等本学科主流期刊上发表学术论文40余篇；福建省科学技术奖二等奖获得者。