[PDF] Top 20 A New Method for Solving Monotone Generalized Variational Inequalities

... the generalized variational inequality problem GVI in the dual ...being monotone function satisfying a certain Lipschitz type condition on ... See full document

... In this paper, a projective splitting method for solving a class of generalized mixed variational inequalities is considered in Hilbert spaces. We investigate a general iterative ... 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

... of variational inequalities is called the mixed variational in- equality involving the nonlinear ...projection method and its variant forms including the Wiener-Hopf equations, descent meth- ... See full document

... Corollary 3.2 see 5, Proposition 3.1. Let H be a real Hilbert space, let C be a closed convex subset of H, and let B : C → H be a β-inverse strongly monotone mapping. Let f : C → C be a contraction with coefficient ... See full document

... for solving varia- tional ...first method, a new iterate is obtained by search- ing the optimal step size along the integrated descent direction from the linear combi- nation of two descent ... See full document

... 19. Kim, JK: Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi- φ -nonexpansive mappings. Fixed Point Theory Appl. 2011, Article ID 10 ... See full document

... for solving a new system of generalized mixed variational inequalities involving different three multi-valued ...a generalized f -projection method for finding the ... See full document

... a new class of general nonlinear implicit variational inequalities, which includes the variational inequalities and variational inclusions in 1–28 as special ...a new ... See full document

... and the general composite explicit one for a strict pseu- docontraction (see (3.3) in [23]) are extended to develop the multistep relaxed explicit extragradient-like one for finding a common element of the set of ... See full document

... of generalized monotone mappings which, in the case of gradient mappings, were related to a generalized convex ...a new concept of relaxed η-α monotonic- ity and obtained the existence for ... See full document

... Variational inequalities and variational inclusions are among the most interesting and important mathematical problems and have been studied intensively in the past years since they have wide ... See full document

... its strong convergence. We also introduced an explicit iterative method as discretization of the implicit method. We proved that both the implicit and the explicit methods con- verge in norm to the same ... See full document

... of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued nonexpansive mappings in the framework of Hilbert ... See full document

... 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 variational ... See full document

... Variational inequalities introduced by Stampacchia [3] in the early sixties have had a great impact and influence in the development of almost all branches of pure and applied sciences and have witnessed an ... See full document

... our new proposed method is that it does not require a pri- ori the knowledge of the Lipschitz constant of F on any bounded subset of C or the strong monotonicity ...the method is proved and a ... See full document

... General variational inequalities involving two operators were introduced and studied by Noor [8] in ...general variational inequalities. General variational inequalities can be ... See full document

... a new class of gener- alized quasi-variational-like inequalities for pseudo-monotone type II operators defined on compact sets in topological vector ...following generalized version of ... See full document

... penalty method for variational inequalities with nonsmooth unbounded operators in Banach space,” Numerical Functional Analysis and Optimization, ...to variational inclusions with accretive ... See full document