Weak and strong convergence theorems for variational inequality problems

In this paper, we study the weak and strong convergence of two algorithms for solving Lipschitz continuous and monotone variational inequalities. The algorithms are inspired by Tseng’s extragradient method and the viscosity method with Armijo-like step size rule. The main advantages of our algorithm...

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Vydáno v:Numerical algorithms Ročník 78; číslo 4; s. 1045 - 1060
Hlavní autoři: Thong, Duong Viet, Hieu, Dang Van
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.08.2018
Springer Nature B.V
Témata:
Algebra
Algorithms
Applied mathematics
Computer Science
Convergence
Efficiency
Hilbert space
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Viscosity
Subgradient extragradient method
65K15
47H10
Viscosity method
68W10
Variational inequality problem
Monotone operator
Extragradient method
47H05
65Y05
Tseng’s extragradient method
ISSN:1017-1398, 1572-9265
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Popis
Shrnutí:In this paper, we study the weak and strong convergence of two algorithms for solving Lipschitz continuous and monotone variational inequalities. The algorithms are inspired by Tseng’s extragradient method and the viscosity method with Armijo-like step size rule. The main advantages of our algorithms are that the construction of solution approximations and the proof of convergence of the algorithms are performed without the prior knowledge of the Lipschitz constant of cost operators. Finally, we provide numerical experiments to show the efficiency and advantage of the proposed algorithms.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0412-z