An inertial subgradient extragradient algorithm with adaptive stepsizes for variational inequality problems. (4th July 2022)

• Record Type: Journal Article
• Authors: Chang, Xiaokai; Liu, Sanyang; Deng, Zhao; Li, Suoping
• Is Part Of: Optimization methods and software. Volume 37:Number 4(2022)
• Page Start: 1507
• Page End: 1526
• Publication Date: 2022-07-04
• Subjects: Variational inequalities -- subgradient extragradient method -- inertial method -- locally Lipschitz continuous -- adaptive step size; 47J20 -- 90C25 -- 90C30 -- 90C52; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1910946
• Languages: English
• ISSNs: 1055-6788

Abstract

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.