稀疏优化理论与算法若干新进展  

Some advances in theory and algorithms for sparse optimization

作　　者：赵晨 罗自炎[1] 修乃华[1] ZHAO Chen;LUO Ziyan;XIU Naihua(School of Science,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《运筹学学报》2020年第4期1-24,共24页Operations Research Transactions

基　　金：国家自然科学基金(Nos.11971052,11771038);北京市自然科学基金(No.Z190002)。

摘　　要：稀疏优化是指带有l0范数正则或稀疏约束的一类重要的非凸非连续优化问题,并被广泛应用于信号和图像处理、机器学习、经济学、统计学等众多领域。经过十多年的发展,稀疏优化已经成为当下热门的研究方向,并已获得丰富的研究成果。为进一步拓展稀疏优化研究,将重点关注最近五年该领域的最新研究成果,并从理论与算法两个方面进行总结与评述,同时列出相关的重要文献以供读者参考。Sparse optimization is an important class of nonconvex and discountinuous optimization problems due to the involved l0 norm regularization or the sparsity constraint.It has wide applications arising in many fields including signal and image processing,machine learning,economics and statistics.Over the past ten years,sparse optimization has attracted much attention and has become a hot research topic,with an accumulation of fruitful research achievements.In order to further promote the research in this direction,we mainly summarize and review the research results in theory and in algorithms during the last five years,along with some related important references,so as to dedicate to the readers.

关 键 词：稀疏优化 l0范数 稀疏集 理论 算法 组稀疏 

分 类 号：O224[理学—运筹学与控制论]