[1]胡立亮,方长杰*.凸优化问题的惯性Uzawa方法[J].四川师范大学学报(自然科学版),2020,43(03):350-356.[doi:10.3969/j.issn.1001-8395.2020.03.010]
 HU Liliang,FANG Changjie.The Inertial Uzawa Methods for Convex Optimization[J].Journal of SichuanNormal University,2020,43(03):350-356.[doi:10.3969/j.issn.1001-8395.2020.03.010]
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凸优化问题的惯性Uzawa方法()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年03期
页码:
350-356
栏目:
基础理论
出版日期:
2020-05-05

文章信息/Info

Title:
The Inertial Uzawa Methods for Convex Optimization
文章编号:
1001-8395(2020)03-0350-07
作者:
胡立亮 方长杰*
重庆邮电大学 理学院, 重庆 400065
Author(s):
HU Liliang FANG Changjie
College of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065
关键词:
凸优化 惯性Uzawa 收敛率 图像去噪
Keywords:
convex optimization inertial Uzawa method convergence rate image denoising
分类号:
O221.2
DOI:
10.3969/j.issn.1001-8395.2020.03.010
文献标志码:
A
摘要:
将惯性项与Uzawa方法相结合,提出一种求解具有线性等式或不等式约束的强凸极小化的惯性Uzawa方法.证明惯性Uzawa方法具有O((1)/(k)) 的收敛速率.最后,给出所提出算法的一些数值实验比较结果.
Abstract:
In this paper, we propose an inertial Uzawa method for solving the strongly convex minimization with linear equality or inequality constraints by combining inertial terms with the Uzawa method. We prove that the convergence rate to a saddle-point is O((1)/(k)) for the inertial Uzawa methods.Finally, we show the efficiency of the proposed methods numerically.

参考文献/References:

[1] NESTEROV Y E. Gradient methods for minimizing composite functions[J]. Math Program,2013,B140(1):125-161.
[2] CAI J F, CANDÈS E J, SHEN Z W. A singular value thresholding algorithm for matrix completion[J]. SIAM J Optim,2010,20(4):1956-1982.
[3] OSHER S, MAO Y, DONG B, et al. Fast linearized Bregman iteration for compressive sensing and sparse denoising[J]. Commun Math Sci,2010,8(1):93-111.
[4] ARROW K J, HURWICZ L, UZAWA H. Studies in Linear and Nonlinear Programming[M]. Stanford Mathematical Studies in the Social Sciences,Vol II. Stanford:Stanford University Press,1958.
[5] BREZZI F, FORTIN M. Mixed and Hybrid Finite Element Methods[M]. Springer Series in Computational Mathematics,Vol 15. New York:Springer-Verlag,1991.
[6] CHAMBOLLE A, POCK T. A first-order primal-dual algorithm for convex problems with applications to imaging[J]. J Math Imaging Vision,2011,40(1):120-145.
[7] ALVAREZ F. On the minimizing property of a second order dissipative system in Hilbert spaces[J]. SIAM J Control Optim,2000,38(4):1102-1119.
[8] ALVAREZ F, ATTOUCH H. An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping[J]. Set-Valued Anal,2001,9(1/2):3-11.
[9] ATTOUCH H, PEYPOUQUET J, REDONT P. A dynamical approach to an inertial forward backward algorithm for convex minimization[J]. SIAM J Optim, 2014,24(1):232-256.
[10] BOT R I, CSETNEK E R, HENDRICH C. Inertial Douglas-Rachford splitting for monotone inclusion problems[J]. Appl Math Comput,2015,256:472-487.
[11] CHEN C, CHAN R H, MA S Q, et al. Inertial proximal ADMM for linearly constrained separable convex optimization[J]. SIAM J Imaging Sci,2015,8(4):2239-2267.
[12] ZHANG L X, FANG C J, CHEN S L. An inertial subgradient-type method for solving single-valued variational inequalities and fixed point problems[J] Numer Algor,2018,79:941-956.
[13] HE B S, MA F, YUAN X M. Convergence study on the symmetric version of ADMM with larger step sizes[J]. SIAM Imaging Sci,2016,9(3):1467-1501.
[14] GOEBEL K,REICH S. Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings [M]. New York:Marcel Dekker,1984.
[15] TAO M, YUAN X M. Accelerated Uzawa methods for convex optimization[J]. Mathematics of Computation,2017,86(306):1821-1845.
[16] ZHU M, CHAN T. An efficient primal-dual hybrid gradient algorithm for total variation image restoration[R]. Los Angeles:UCLA,Center for Appliend Math,CAM Reports,2008(1):1-29.
[17] NESTEROV Y E. Smooth minimization of non-smooth functions[J]. Math Program,2005,A103(1):127-152.

备注/Memo

备注/Memo:
收稿日期:2018-11-22 接受日期:2019-03-05 基金项目:国家自然科学基金(11771350)和重庆市自然科学基金基础与前沿研究计划(CSTC2016JCYJA0163和CSTC2018JCYJAX0605) *通信作者简介:方长杰(1974-),男,教授,主要从事数值分析、优化算法及其应用的研究,E-mail:fangcj@cqupt.edu.cn
更新日期/Last Update: 2020-05-05