[PDF] Top 20 Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems

... known variational in- equality problem (VIP), which find lots of applications in sparse reconstruction, image reconstruction, traffic and transportation systems, is to get x ∗ ∈ C with Ax ∗ , x – x ∗ ≥ 0 ∀ x ∈ ... See full document

... Variational inequalities introduced by Stampacchia 1 in the early sixties have had a great impact and influence in the development of almost all branches of pure and applied ...the variational ... See full document

... to point out that if the considered mapping T is (κ, θ )-relaxed cocoercive and γ -Lipschitz mapping such that θ > κγ  , then it must be a (θ – κγ  )-strongly monotone ... See full document

... relaxed extragradient method in the setting of uniformly convex and -uniformly smooth Banach spaces, and then another explicit iterative algorithm in the setting of uniformly convex Banach spaces with a uniformly ... See full document

... Let H be a real Hilbert space with the inner product · , · and the norm · . Let C be a nonempty, closed and convex subset of H, and let T : C → C be a nonlinear mapping. Throughout this paper, we use F(T ) to denote the ... See full document

... the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications ... See full document

... of fixed points of a family of finitely nonexpansive mappings, the set of solutions of mixed equilibrium problem and the set of solutions of a variational inequality problem for a β-inverse-strongly ... See full document

... Denote the set of solutions of MEP by . The MEP includes fixed point problems, opti- mization problems, variational inequality problems, Nash EPS and the EP as special cases. Recall that ... See full document

... fixed point problem of a finite family of strict pseudo-contraction mappings instead of SVIP ...fixed point problem of a finite family of strict pseudo-contraction ... See full document

... Korpelevich’s extragradient method has extensively been studied in the literature for solving a more general problem that consists of finding a common point that lies in the solution set of a ... See full document

... 18. Yamada, I: The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. In: Butnariu, D, Censor, Y, Reich, S (eds.) ... See full document

... s extragradient method [6], Nadezh- kina and Takahashi [7] introduced an iterative scheme, called extragradient method, for finding an element of F(S) ∩ Ω and established the weak convergence ...a ... See full document

... hybrid extragradient iterative method for finding a common element of the set of points satisfying the Ky Fan inequalities, variational inequality and the set of fixed points of a strict ... See full document

... paper, fixed point problems of nonexpansive mappings and solution problems of generalized variational inequalities are investigated based on a viscosity approximate iterative ... See full document

... hybrid extragradient method for finding a common element of the solution set of a variational inequality problem, the solution set of a general system of variational inequalities, and the ... See full document

... the variational inequality problem involving monotone operator and the fixed point problem of a quasi-nonexpansive mapping with a demiclosedness property in a real Hilbert ...a subgradient ... 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

... fixed point principles for set-valued ...fixed point theorem (which is equivalent to the Knaster-Kuratowski-Mazurkiewicz-Ky Fan principle) much as in [] and relies heav- ily on ...the point-to-set map ... See full document

... of fixed points of a demicontractive mapping and the set of solutions of a mixed equilibrium ...an extragradient method for solving the mixed equilibrium problems and the fixed point ... See full document

... so-called extragradient method motivated by the idea of Korpeleviˇc [9] for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational ... See full document