Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
Modified Projection-Type Methods for Monotone Variational Inequalities
SIAM Journal on Control and Optimization
A class of iterative methods for solving nonlinear projection equations
Journal of Optimization Theory and Applications
Improvements of some projection methods for monotone nonlinear variational inequalities
Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications
A new modified Goldstein-Levitin-Polyakprojection method for variational inequality problems
Computers & Mathematics with Applications
A note on a globally convergent Newton method for solving monotone variational inequalities
Operations Research Letters
Computers & Mathematics with Applications
Some projection methods with the BB step sizes for variational inequalities
Journal of Computational and Applied Mathematics
Hi-index | 0.09 |
In this paper, we propose a new projection method for solving variational inequality problems, which can be viewed as an improvement of the method of Han and Lo [D.R. Han, Hong K. Lo, Two new self-adaptive projection methods for variational inequality problems, Computers & Mathematics with Applications 43 (2002) 1529-1537], by adopting a new step-size rule. The method is as simple as Han and Lo's methods [D.R. Han, Hong K. Lo, Two new self-adaptive projection methods for variational inequality problems, Computers & Mathematics with Applications 43 (2002) 1529-1537] and other extra-gradient-type methods, which uses only function evolutions and projections onto the feasible set. We prove that under the condition that the underlying function is co-coercive, the sequence generated by the method converges to a solution of the variational inequality problem globally. Some preliminary computational results are reported, which illustrated that the new method is more efficient than Han and Lo's method [D.R. Han, Hong K. Lo, Two new self-adaptive projection methods for variational inequality problems, Computers & Mathematics with Applications 43 (2002) 1529-1537].