Local convergence analysis of projection-type algorithms: unified approach
Journal of Optimization Theory and Applications
Some new projection methods for variational inequalities
Applied Mathematics and Computation
Some recent advances in projection-type methods for variational inequalities
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Singularities of Monotone Vector Fields and an Extragradient-type Algorithm
Journal of Global Optimization
A new double projection algorithm for variational inequalities
Journal of Computational and Applied Mathematics
A simple self-adaptive alternating direction method for linear variational inequality problems
Computers & Mathematics with Applications
A new class of projection and contraction methods for solving variational inequality problems
Computers & Mathematics with Applications
An algorithm for generalized variational inequality with pseudomonotone mapping
Journal of Computational and Applied Mathematics
A superlinearly convergent projection method for constrained systems of nonlinear equations
Journal of Global Optimization
An inexact-restoration method for nonlinear bilevel programming problems
Computational Optimization and Applications
An algorithm for solving the obstacle problems
Computers & Mathematics with Applications
A new double projection algorithm for variational inequalities
Journal of Computational and Applied Mathematics
The numerical solution of obstacle problem by self adaptive finite element method
WSEAS Transactions on Mathematics
Weighted variational inequalities in non-pivot Hilbert spaces with applications
Computational Optimization and Applications
Korpelevich's method for variational inequality problems in Banach spaces
Journal of Global Optimization
Computers & Mathematics with Applications
Monotonicity of NFP mappings associated with variational
AMERICAN-MATH'12/CEA'12 Proceedings of the 6th WSEAS international conference on Computer Engineering and Applications, and Proceedings of the 2012 American conference on Applied Mathematics
A projected subgradient method for solving generalized mixed variational inequalities
Operations Research Letters
Korpelevich's method for variational inequality problems on Hadamard manifolds
Journal of Global Optimization
Two-step projection methods for a system of variational inequality problems in Banach spaces
Journal of Global Optimization
A smoothing homotopy method for variational inequality problems on polyhedral convex sets
Journal of Global Optimization
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We propose a new projection algorithm for solving the variational inequality problem, where the underlying function is continuous and satisfies a certain generalized monotonicity assumption (e.g., it can be pseudomonotone). The method is simple and admits a nice geometric interpretation. It consists of two steps. First, we construct an appropriate hyperplane which strictly separates the current iterate from the solutions of the problem. This procedure requires a single projection onto the feasible set and employs an Armijo-type linesearch along a feasible direction. Then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the halfspace containing the solution set. Thus, in contrast with most other projection-type methods, only two projection operations per iteration are needed. The method is shown to be globally convergent to a solution of the variational inequality problem under minimal assumptions. Preliminary computational experience is also reported.