An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems

In this paper, we introduce an efficient subgradient extragradient (SE) based method for solving variational inequality problems with monotone operator in Hilbert space. In many existing SE methods, two values of operator are needed over each iteration and the Lipschitz constant of the operator or l...

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Vydáno v:Optimization methods & software Ročník 37; číslo 4; s. 1507 - 1526
Hlavní autoři: Chang, Xiaokai, Liu, Sanyang, Deng, Zhao, Li, Suoping
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 04.07.2022
Taylor & Francis Ltd
Témata:
Adaptive algorithms
adaptive step size
Hilbert space
inertial method
Iterative methods
locally Lipschitz continuous
Mathematical analysis
subgradient extragradient method
Variational inequalities
ISSN:1055-6788, 1029-4937
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Abstract In this paper, we introduce an efficient subgradient extragradient (SE) based method for solving variational inequality problems with monotone operator in Hilbert space. In many existing SE methods, two values of operator are needed over each iteration and the Lipschitz constant of the operator or linesearch is required for estimating step sizes, which are usually not practical and expensive. To overcome these drawbacks, we present an inertial SE based algorithm with adaptive step sizes, estimated by using an approximation of the local Lipschitz constant without running a linesearch. Each iteration of the method only requires a projection on the feasible set and a value of the operator. The numerical experiments illustrate the efficiency of the proposed algorithm.
AbstractList In this paper, we introduce an efficient subgradient extragradient (SE) based method for solving variational inequality problems with monotone operator in Hilbert space. In many existing SE methods, two values of operator are needed over each iteration and the Lipschitz constant of the operator or linesearch is required for estimating step sizes, which are usually not practical and expensive. To overcome these drawbacks, we present an inertial SE based algorithm with adaptive step sizes, estimated by using an approximation of the local Lipschitz constant without running a linesearch. Each iteration of the method only requires a projection on the feasible set and a value of the operator. The numerical experiments illustrate the efficiency of the proposed algorithm.
Author Liu, Sanyang
Li, Suoping
Deng, Zhao
Chang, Xiaokai
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  givenname: Suoping
  surname: Li
  fullname: Li, Suoping
  organization: Lanzhou University of Technology
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SubjectTerms Adaptive algorithms
adaptive step size
Hilbert space
inertial method
Iterative methods
locally Lipschitz continuous
Mathematical analysis
subgradient extragradient method
Variational inequalities
Title An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems
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