[PDF] Top 20 An Implicit Extragradient Method for Hierarchical Variational Inequalities

... Recently, hierarchical fixed point problems and hierarchical minimization problems have attracted many authors’ attention due to their link with some convex programming ...following hierarchical ... See full document

... descent extragradient algorithm and another multi-step composite Mann-type viscosity iterative algorithm for finding a solution of triple hierarchical variational inequalities de- fined over the ... See full document

... On the other hand, for finding an element of F ix(S), Takahashi et al., [17] introduced the following iteration procedure which is usually called the shrinking projection method. Let C be nonempty closed convex ... See full document

... hT u, g(v) − g(u)i ≥ 0, ∀v ∈ H : g(v) ∈ K, (2.2) which is known as the general variational inequality, introduced and studied by Noor [8] in 1988. For the applications, numerical methods, formulation and other ... See full document

... On the other hand, let F : H → H be a κ-Lipschitzian and η-strongly monotone operator with constants κ, η > 0, and let T : H → H be nonexpansive such that FixT / ∅. In 2001, Yamada 6 introduced the so-called hybrid ... See full document

... Let H be a real Hilbert space whose inner product and norm are denoted by 〈·,·〉 and || · ||, respectively, and let C be a nonempty closed convex subset of H. Corresponding to an operator A : C ® H and set C, the ... See full document

... an implicit iterative method and an explicit iterative method for solving a general system of variational inequalities (in short, GSVI) in X based on Korpelevich’s extragradient ... See full document

... the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the ... See full document

... iterative method in this paper is introduced for solving a system of variational inequalities with fixed-point set constraints. Under suitable conditions, strong conver- gence results are proved in ... See full document

... Korpelevich?s extragradient method, the viscosity approximation method, the hybrid steepest-descent method [] and Mann?s it- eration ... See full document

... the variational inequality ...hybrid extragradient method based on the well-known extragradient method, viscosity approximation method, and Mann-type iteration method, ... See full document

... generalized variational inequalities find application in economics and transporta- tion equilibrium, engineering sciences, ...extra-gradient method [, ] is a popular solu- tion method, which ... See full document

... viscosity method for hierarchically approximating some common fixed point of an infinite family of nonexpansive mappings and prove the strong convergence theorems for solving some variational inequality ... See full document

... quasi-variational inequalities, which is called the general nonconvex quasi-variational inequality on the uniformly prox-regular sets, It is well-known [3,24] that the prox-regular sets are nonconvex ... See full document

... “An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings,” Nonlinear ... See full document

... Colao, V, Acedo, GL, Marino, G: An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexp[r] ... See full document

... We denote the set of solutions of GMEP (.) by GMEP(Θ, ϕ, A). The GMEP (.) is very general in the sense that it includes, as special cases, optimization problems, variational in- equalities, minimax problems, ... See full document

... Bilevel variational inequalities are special classes of qua- sivariational inequalities (see [2, 4, 18, 37]) and of equilib- rium with equilibrium constraints considered in [30, ...[34]), ... See full document

... Huang [] studied problem (.) in the case where R is maximal monotone and B is strongly monotone and Lipschitz continuous with D(R) = C = H. Zeng et al. [] further studied problem (.) in a more general setting ... See full document

... the variational inequalities are equivalent to the fixed-point problems, the origin of which can be traced back to Lions and Stampacchia ...iterative method for solving variational ... See full document