Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Mathematical Programming: Series A and B
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
A new method for a class of linear variational inequalities
Mathematical Programming: Series A and B
Matrix computations (3rd ed.)
New alternating direction method for a class of nonlinear variational inequality problems
Journal of Optimization Theory and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
A proximal decomposition algorithm for variational inequality problems
Journal of Computational and Applied Mathematics
A simple self-adaptive alternating direction method for linear variational inequality problems
Computers & Mathematics with Applications
Hi-index | 0.00 |
The alternating direction method solves large scale variational inequality problems with linear constraints via solving a series of small scale variational inequality problems with simple constraints. The algorithm is attractive if the subproblems can be solved efficiently and exactly. However, the subproblem is itself variational inequality problem, which is structurally also difficult to solve. In this paper, we develop a new decomposition algorithm, which, at each iteration, just solves a system of well-conditioned linear equations and performs a line search. We allow to solve the subproblem approximately and the accuracy criterion is the constructive one developed recently by Solodov and Svaiter. Under mild assumptions on the problem's data, the algorithm is proved to converge globally. Some preliminary computational results are also reported to illustrate the efficiency of the algorithm.