[1]葛志利,蔡邢菊,张欣.算子分裂法求解一类变分不等式问题的收敛率分析[J].南京师范大学学报(自然科学版),2020,43(01):5-12.[doi:10.3969/j.issn.1001-4616.2020.01.002]
　GeZhili,CaiXingju,ZhangXin.ConvergenceRateAnalysisofAnOperatorSplittingMethodforSolvingaClassofVariationalInequalityProblems[J].JournalofNanjingNormalUniversity(NaturalScienceEdition),2020,43(01):5-12.[doi:10.3969/j.issn.1001-4616.2020.01.002]
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算子分裂法求解一类变分不等式问题的收敛率分析()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年01期
页码:
5-12
栏目:
·数学·
出版日期:
2020-03-15

文章信息/Info

Title:
ConvergenceRateAnalysisofAnOperatorSplittingMethodforSolvingaClassofVariationalInequalityProblems
文章编号:
]1001-4616(2020)01-0005-08
作者:
葛志利1; 蔡邢菊2; 张欣3
(1.南京科技职业学院基础科学部,江苏南京210048)(2.南京师范大学数学科学学院,江苏南京210023)(3.宿迁学院文理学院,江苏宿迁223800)
Author(s):
GeZhili1; CaiXingju2; ZhangXin3
(1.BasicSciencesDepartment,NanjingPolytechnicInstitute,Nanjing210048,China)(2.SchoolofMathematicalSciences,NanjingNormalUniversity,Nanjing210023,China)(3.SchoolofArtsandScience,SuqianCollege,Suqian223800,China)
关键词:
部分算子未知; 单调变分不等式; 算子分裂法; 次线性收敛率
Keywords:
partiallyunknownmappings; monotonevariationalinequalities; operatorsplittingmethod; sublinearconvergencerate
分类号:
O221.4
DOI:
10.3969/j.issn.1001-4616.2020.01.002
文献标志码:
A
摘要:
考虑一类变分不等式问题:寻找x*∈Ω,满足F(x*)T(x-x*)≥0,x∈Ω,其中Ω是Rn上的闭凸子集,F=f+g是Rn到Rn的连续算子,f和g单调但f的表达式未知.针对此类应用较广的问题,本文研究了一种新的算子分裂法.根据已有的收敛性结果,进一步分析了该方法在非遍历意义下O(1/k)和o(1/k)的次线性收敛率,其中k表示迭代步数.最后,通过数值实验展示了算法的有效性.
Abstract:
Consideraclassofvariationalinequalityproblems:findingx*∈Ω,suchthatF(x*)T(x-x*)≥0,x∈Ω,whereΩRnisnonempty,closedandconvex,F=f+gisacontinuousmappingfromRntoRn,fandgaremonotonebutfisunknown.Westudyanoperatorsplittingmethodforthisclassofproblemswithavarietyofapplications.Basedonthepreviousconvergenceresults,wefurtheranalyzetheO(1/k)ando(1/k)sublinearconvergencerateinnon-ergodicsenseforthisoperatorsplittingmethod,wherekcountstheiterationnumber.Finally,numericalresultsdemonstratetheefficiencyofthealgorithm.

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备注/Memo

备注/Memo:
收稿日期:2019-03-31.
基金项目:国家自然科学基金项目(11401315、11871279)、江苏省高校自然科学研究面上项目(17KJD110003)、江苏省高职院校教师专业带头人高端研修项目和江苏省青蓝工程资助项目.
通讯作者:葛志利,博士,研究方向:运筹学与控制论.E-mail:gezhilyly66@126.com
更新日期/Last Update: 2020-03-15