Modified extragradient-like algorithms with new stepsizes for variational inequalities

Dang Hieu (), Pham Ky Anh () and Le Dung Muu ()
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Dang Hieu: Ton Duc Thang University
Pham Ky Anh: Vietnam National University, Hanoi
Le Dung Muu: Thang Long University

Computational Optimization and Applications, 2019, vol. 73, issue 3, No 8, 913-932

Abstract: Abstract The paper concerns with an algorithm for approximating solutions of a variational inequality problem involving a Lipschitz continuous and monotone operator in a Hilbert space. The algorithm uses a new stepsize rule which does not depend on the Lipschitz constant and without any linesearch procedure. The resulting algorithm only requires to compute a projection on feasible set and a value of operator over each iteration. The convergence and the convergence rate of the algorithm are established. Some experiments are performed to show the numerical behavior of the proposed algorithm and also to compare its performance with those of others.

Keywords: Variational inequality; Monotone operator; Extragradient method; Subgradient extragradient method; Projection method; 65Y05; 65K15; 68W10; 47H05; 47H10 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-019-00093-x

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