稀疏优化二阶算法研究进展  

PROGRESS OF SECOND-ORDER METHODS FOR SPARSE OPTIMIZATION

作　　者：王锐 修乃华[2] Wang Rui;Xiu Naihua(Beijing International Center for Mathematical Research,Peking University,Beijing 100871,China;Department of Mathematics,School of Science,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京大学北京国际数学研究中心,北京100871 [2]北京交通大学理学院数学系,北京100044

出　　处：《数值计算与计算机应用》2022年第3期314-328,共15页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11971052,12131004);北京自然科学基金(Z190002)资助。

摘　　要：稀疏优化是最优化学科近十余年发展起来的一个崭新分支.它主要研究带有稀疏结构特征的优化问题,在大数据分析与处理、机器学习与人工智能、信号与图像处理、生物信息学等学科领域有广泛应用.然而,稀疏优化属于非凸非连续优化,是一个NP-难问题.一直以来,人们通常采用一阶算法求解大规模稀疏优化问题,并取得了丰富成果.为提高计算速度和求解精度,人们近几年创新发展了若干计算花费少的二阶算法,本文主要介绍与评述其研究进展,奉献给读者.Sparse optimization developed in the past ten years is a new branch of the optimization discipline.It mainly studies optimization problems with sparse structure characteristics,and is widely applied to many fields including machine learning and artificial intelligence,signal and image processing,bioinformatics.However,sparse optimization problem is nonconvex,noncontinuous and even NP-hard.First-order algorithms are commonly used to solve largescale sparse optimization problems,and have achieved rich results.In order to improve the calculation speed and solution accuracy,a number of second-order algorithms with low computational cost have been developed in recent years.This paper mainly introduces its research progress and is dedicated to readers.

关 键 词：稀疏优化 二阶算法 正则项 收敛性 

分 类 号：O224[理学—运筹学与控制论]