[PDF] Top 20 A modified subgradient extragradient method for solving monotone variational inequalities

... The variational inequality problem VI(C, f ) has re- ceived much attention due to its applications in a large variety of problems arising in struc- tural analysis, economics, optimization, operations research and ... See full document

... Corollary 7. Let C be a nonempty, closed and convex subset of a real Hilbert space H , let F be a bifunction F : C× C into R satisfying conditions (A1) − (A5), let A be an α-inverse-strongly monotone mapping of C ... See full document

... This algorithm incorporate the inertial terms in the projection and contraction algorithm, which does not need the summability condition for the sequence. The fourth one was a self-adaptive algorithm which was based on ... See full document

... maximal monotone and B is strongly monotone and Lipschitz continuous with D(R) = C = ...for solving variational inclusions have been further studied and developed; for more details, refer to ... See full document

... quasi-monotone variational inequalities in infinite-dimensional Hilbert ...the extragradient method for solving semistrictly quasi-monotone variational ... See full document

... maximal monotone and B is strongly monotone and Lipschitz-continuous with D(R) = C = ...for solving variational inclusions have been further studied and developed; for more details, refer to ... See full document

... explicit extragradient-like one for finding a common element of the set of solutions of the CMP (3) for a convex functional f : C → R with L- Lipschitz continuous gradient ∇ f , the set of solutions of a finite ... See full document

... This method overcomes the difficulties arising in the project gradient method by performing an additional forward step and a projection at each iter- ation according to double ...the extragradient ... 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

... regularization method is an important approach to the ...Tikhonov method with generalized reg- ularization operators and bifunctions is extended to pseudomonotone variational inequalities and ... See full document

... a variational inequality problem for a monotone and Lipschitz continuous ...an extragradient-like iterative algorithm that is based on the extragradient-like approximation method and ... See full document

... inertial subgradient–extragradient algorithms with a line-search process for solving the VIP with pseudomonotone and Lipschitz continuous mapping and the CFPP of finitely many nonexpansive mappings ... See full document

... The variational inequality problem is a fundamental problem in variational analysis and, in particular, in optimization ...gradient method for constrained optimization, ... See full document

... is monotone and Lipschitz. However, the weakness of this extragradient method is that one needs to calculate two projections onto C in each iteration ...the subgradient extragradient ... See full document

... Let C be a nonempty closed convex subset of a real Hilbert space H . Let S : C ® C be an asymptotically nonexpansive map in the intermediate sense with the fixed point set F ( S ). Let A : C ® H be a Lipschitz continuous ... See full document

... the extragradient method, we introduce an iterative method for finding an element of the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous ... See full document

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

... for solving the variational inequalities in real Hilbert spaces, denoted by VI(C, ...the method is proved and a posteriori error estimate of the convergence rate is ... See full document

... inverse variational inequalities, which can be widely used to study the problems in economics, network and transportation, ...inverse variational inequality arises from the transportation sys- tem ... See full document

... modified subgradient extragradient method, projection method, viscosity approximation method, and Schrödinger mapping and strongly positive bounded Schrödinger operator approaches to ... See full document