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Projected Subgradient Method under Sparsity Constraints

发布时间:2021-09-17 作者:77779193永利官网 浏览次数:
Speaker: 李松 DateTime: 2021年9月23日(周四)上午11:00-12:00
Brief Introduction to Speaker:

李松,浙江大学二级教授,求是特聘教授。主要从事应用调和分析及相关领域的研究工作,其中包括:压缩感知、低秩矩阵恢复、小波分析理论与应用、相位恢复、盲去卷积等。到目前为止在国际数学、应用数学、数学与信息交叉以及数学与信号处理交叉等领域著名期刊发表了90余篇学术论文;主持了包括国家自然科学基金重点项目、面上项目以及浙江省重大科技项目等7项基金项目,作为第一完成人曾获得教育部自然科学二等奖(2013)。目前指导毕业了13位博士研究生,20余位硕士研究生,其中;博士毕业生中1人获得国家自然科学优秀青年基金资助(2020)、此外,作为合作导师指导的博士后获得国家自然科学优秀青年基金资助(2014)。

Place: 腾讯会议会议号591500143
Abstract:In this talk, a projected subgradient method under sparsity constraints is proposed to solve the general convex model and some convergence results are established. A stronger convergence theorem for strongly convex functions without assumption on differentiable condition is also established. Furthermore, the corresponding stochastic projected subgradient method is provided with convergence guarantee. In our settings, BIHT is a special case of the projected subgradient method. Therefore, the convergence analysis can be applied to BIHT naturally. Then, we apply the projected subgradient method to some related non-convex optimization models arising in compressive sensing with 1-constraint, sparse support vector machines, and rectifier linear units regression. Finally, some numerical examples are presented to show the validity of our convergence analysis. The numerical experiments also show that the proposed projected subgradient method is very simple to implement, robust to sparse nois...