关于举行彭定涛教授（贵州大学）学术报告的通知

报告题目: Fixed point continuation algorithm with extrapolation for Schatten p-quasi-norm regularized matrix optimization problems

报  告  人: 彭定涛 教授

报告时间: 2023年 12月18日（星期一）10:00-11:00              

报告地点：37号楼3A02

邀  请  人: 潘少华  教授

数学学院

2023年12月13日

报告摘要：In this report, we consider a general low-rank matrix optimization problem which is modeled by a general Schatten p-quasi-norm (0<p<1) regularized matrix optimization. For this nonconvex nonsmooth and non-Lipschitz matrix optimization problem, based on the matrix p-thresholding operator, we first propose a fixed point continuation algorithm with extrapolation (FPCAe) for solving it. Secondly, we prove that any accumulation point of the iterative sequence generated by the proposed algorithm is not only a critical point but also a global stationary point of the problem, where the global stationary point possesses some global optimality which can exclude too many stationary points even some local minimizers of the nonconvex problem. We also prove the rank invariance of the iterative sequence. Thirdly, we prove the global convergence and R-linear convergence rate of the whole iterative sequence generated by the proposed algorithm under some mild conditions. Finally, we conduct a large number of numerical experiments on random square and rectangular matrix completion problem, greyscale image and three-channel image recovery problem. The numerical results illustrate that the proposed FPCAe algorithm is competitive with some state-of-the-art algorithms for low-rank matrix recovery in terms of speed, accuracy, robustness and anti-noise. 

报告人简介：彭定涛，博士，教授，贵州大学一流学科特聘教授，博士生导师，中国运筹学会数学规划分会常务理事，贵州省应用统计学会常务理事，贵州省数学学会理事，贵州省优秀高层次留学回国人才，国家自然科学基金通信评审专家，国家科学技术奖励专家库入库专家，教育部全国研究生教育评估监测专家。主要研究领域：最优化理论与方法、非线性分析和博弈论。多次受邀访问香港理工大学应用数学系，受聘Research Fellow等职。近年来，主持省部级以上项目10余项，其中国家自然科学基金3项。在COAP、JOGO、JOTA、NA.TMA、SCM等国内外数学期刊上发表论文60余篇。曾获贵州大学“优秀青年教师”、“我心目中的好老师”、“国华奖优秀教师”、“大北农奖优秀教师”、“我心目中的好导师”等荣誉，2017年获贵州大学教学成果特等奖，2018年获贵州省高等教育教学成果一等奖，2022年获贵州省自然科学奖三等奖、贵州省高等教育教学成果二等奖。