[1]余 静,夏福全*.一类混合变分不等式的可变度量惯性近似点算法[J].四川师范大学学报(自然科学版),2019,(05):590-597.[doi:10.3969/j.issn.1001-8395.2019.05.004]
 YU Jing,XIA Fuquan.A Class of Variable Metric Inertial Proximal Point Algorithms for Mixed Variational Inequalities[J].Journal of SichuanNormal University,2019,(05):590-597.[doi:10.3969/j.issn.1001-8395.2019.05.004]
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一类混合变分不等式的可变度量惯性近似点算法()
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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:
期数:
2019年05期
页码:
590-597
栏目:
基础理论
出版日期:
2019-07-15

文章信息/Info

Title:
A Class of Variable Metric Inertial Proximal Point Algorithms for Mixed Variational Inequalities
文章编号:
1001-8395(2019)05-0590-08
作者:
余 静 夏福全*
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
YU Jing XIA Fuquan
College of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
混合变分不等式 变尺度 惯性近似点算法
Keywords:
mixed variational inequalities variable metric inertial proximal point algorithms
分类号:
O176; O178
DOI:
10.3969/j.issn.1001-8395.2019.05.004
文献标志码:
A
摘要:
提出求解混合变分不等式问题的可变度量惯性近似点算法,该算法结合了经典的近似点算法和惯性算法,并且在算法的每一步中,采用了可变正定矩阵,该可变正定矩阵可诱导出可变度量.在合适的假设条件下,证明算法的全局收敛性以及非线性O(1/k)收敛率.研究混合变分不等式的解集为空集与该算法所得到的序列无界性之间的关系.
Abstract:
Firstly, we present a variable metric inertial proximal point algorithm, combined by classic proximal point method and inertial method for a solving mixed variational inequality problem.At each step of the algorithm, we use the variable positive definite metric which could define a variable metric.Secondly, under suitable assumptions, we establish the global convergence and nonasymptotic nvergence rate for the proposed algorithm.Finally, we show the relation between the empty solution set of the mixed variational inequality and the unbounded sequence obtained by our algorithm.

参考文献/References:

[1] PARENTE L A, LOTITO P A, SOLODOV M V.A class of inexact variable metric proximal point algorithms[J].SIAM J Optim,2008,19(1):240-260.
[2] ALVAREZ F, ATTOUCH H.An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping[J].Set Valued Analysis,2001,9(1/2):3-11.
[3] ALVAREZ F.Weak convergence of a relaxed and inertial hybrid projection-proximal point algorithm for maximal monotone operators in Hilbert space[J].SIAM J Optim,2010,14(3):773-782.
[4] CHEN C H, MA S Q, YANG J F.A general inertial proximal point algorithm for mixed variational inequality problem[J].SIAM J Optim,2015,25(4):2120-2142.
[5] HAN D R, XU W, YANG H.An operator splitting method for variational inequalities with partially unknown mappings[J].Numer Math,2008,111(2):207-237.
[6] 林贵华.非线性最优化基础[M].北京:科学出版社,2011.

相似文献/References:

[1]陈熙德.一类新的混合变分不等式[J].四川师范大学学报(自然科学版),1999,(02):8.
 Chen Xide (Basic Science and Technology Department,Sichuan Institute of Animal Husbandry & Veterinary Medicine,Rongchang 00,et al.[J].Journal of SichuanNormal University,1999,(05):8.

备注/Memo

备注/Memo:
收稿日期: 2017-12-21 接受日期: 2018-03-16
基金项目: 教育部科学技术重点项目(212147)
*通信作者简介:夏福全(1973—),男,教授,主要从事最优化理论及应用研究,E-mail:fuquanxia@163.com
更新日期/Last Update: 2019-07-15