一个无需Lipschitz连续性的混合自适应共轭梯度投影法及其应用  

Gradient Projection Method Without Lipschitz Continuity and Its Applications

作　　者：袁梓航 王云 刘鹏杰 卓越 周金诚 YUAN Zihang;WANG Yun;LIU Pengjie;ZHUO Yue;ZHOU Jincheng(School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China;Department of Civil and Environmental Engineering,The Hong Kong Polytechnic University,Kowloon 999077,China)

机构地区：[1]中国矿业大学数学学院,江苏徐州221116 [2]香港理工大学土木及环境工程学系,中国香港九龙999077

出　　处：《应用数学》2023年第4期951-960,共10页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(72071202);Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX22_2491);Graduate Innovation Program of China University of Mining and Technology(2022WLKXJ021);Undergraduate Training Program for Innovation and Entrepreneurial,China University of Mining and Technology(202210290205Y)。

摘　　要：共轭梯度投影法是求解大规模凸约束非线性单调方程组的有效算法之一.该文基于四个经典共轭参数,采用混合策略及投影技术,提出一个有效的混合自适应共轭梯度投影法.该方法产生的搜索方向独立于任何线搜索满足充分下降性和信赖域性质.无需Lipschitz连续性假设,分析并证明新方法的全局收敛性.数值结果验证所提方法的计算有效性.最后,通过稀疏信号恢复试验,验证新方法的实用性.The conjugate gradient projection method is an effective algorithm for solving large-scale nonlinear monotone equations with convex constraints.In this paper,based on the four classical conjugate parameters,an effective hybrid self-adaptive conjugate gradient projection method is proposed by using hybridization strategy and projection technique.The search direction satisfies the sufficient descent and trust region properties independent of any line search.The global convergence of the new method is analyzed and proved without the Lipschitz continuity assumption.The results of the numerical experiments show the computational efficiency of the proposed method.Finally,the applicability of the new method is verified by some numerical experiments on sparse signal restoration.

关 键 词：非线性单调方程组 共轭梯度投影法 收敛性 压缩感知 

分 类 号：O221[理学—运筹学与控制论]