Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. St...

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Bibliographic Details
Published inJournal of global optimization Vol. 82; no. 3; pp. 523 - 557
Main Authors Tan, Bing, Qin, Xiaolong, Yao, Jen-Chih
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2022
Springer
Subjects
Algorithms
Computer Science
Equality
Mathematics
Mathematics and Statistics
Medical colleges
Methods
Operations Research/Decision Theory
Optimization
Real Functions
Subgradient extragradient method
65K15
47J20
Optimal control problem
Variational inequality problem
47H09
Inertial method
47H05
Pseudomonotone mapping
49J15
Projection and contraction method
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Summary:This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-021-01095-y