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Rouhani, Behzad Djafari; Mohebbi, Vahid

A variant of the extragradient method for approximating solutions of pseudo-monotone quasi-variational inequalities. (English) Zbl 07920742

Discrete Contin. Dyn. Syst., Ser. S 17, No. 10, 3116-3128 (2024).
Summary: In this paper, we study a variant of the extragradient method for solving quasi-variational inequality problems in Hilbert spaces. In fact, we assume that the given operator is pseudo-monotone and Lipschitz continuous, and the given multivalued mapping is quasi-nonexpansive with nonempty, closed and convex values. Then by modifying the so-called extragradient method (an explicit discretization of a dynamical system) and using the Halpern’s regularization method, we show that the generated sequence is strongly convergent to a solution of the quasi-variational inequality problem, without any knowledge of the Lipschitz constant of the operator. Finally, we give some examples of applications and numerical experiments of our main result.

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MSC:

47J20 Variational and other types of inequalities involving nonlinear operators (general)
58E35 Variational inequalities (global problems) in infinite-dimensional spaces
65K15 Numerical methods for variational inequalities and related problems
90C30 Nonlinear programming

Keywords:

extragradient method; Lipschitz continuous; pseudo-monotone operator; quasi-nonexpansive mapping; quasi-variational inequality
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References:

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