An inexact operator splitting method for general mixed variational inequalities

Abstract

The present paper aims to deal with an inexact implicit method with a variable parameter for general mixed variational inequalities in the setting of real Hilbert spaces. Under standard assumptions, the global convergence of the proposed method is proved. Numerical example is presented to illustrate the proposed method and convergence result. The results and method presented in this paper generalize, extend and unify some known results in the literature.Keywords: General mixed variational inequalities implicit methods resolvent operator inexact methods self-adaptive rules. MSC: 65K10, 90C25, 90C30.where H is a real Hilbert space, whose inner product and norm are denoted by •, • and • respectively and F, h : H → H are two nonlinear operators. Let ∂ϕ denotes the subdierential of function ϕ, where ϕ : H → R ∪ {∞} is a proper convex lower semi continuous function on H. GMVI includes many important optimization problems as special cases: