Modified extragradient method with Bregman distance for variational inequalities

• Published in: Applicable analysis Vol. 101; no. 2; pp. 655 - 670
• Main Authors: Van Hieu, Dang, Cholamjiak, Prasit
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 22.01.2022; Taylor & Francis Ltd
• Subjects: Algorithms; Bregman projection; extragradient method; Hilbert space; Iterative methods; Mathematical analysis; monotone operator; Numerical methods; Projection; Variational inequality
• ISSN: 0003-6811; 1563-504X
• DOI: 10.1080/00036811.2020.1757078

The paper deals with a numerical method for solving a monotone variational inequality problem in a Hilbert space. The algorithm is inspired by Popov's modified extragradient method and the Bregman projection with a simple stepsize rule. Applying Bregman projection allows the algorithm to be more flexible in computations when choosing a projection. The stepsizes, which vary from step to step, are found over each iteration by a cheap computation without any linesearch. The convergence of the algorithm is proved without the prior knowledge of Lipschitz constant of the operator involved. Some numerical experiments are performed to illustrate the computational performances of the new algorithm with several known Bregman distances. The obtained results in this paper extend some existing results in the literature.