We give, for a class of monotone affine variational inequality problems, a simple characterization of when a certain residual function provides a bound on the distance from any feasible point to the solution set. This result has implications on the global linear convergence of a certain projection algorithm and of matrix splitting algorithms using regular splitting.
Bibliographical noteFunding Information:
* The research of the first author is supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. OPG0090391. Correspondence to: Paul Tseng, Department of Mathematics, GN-50, University of Washington, Seattle, WA 98195, USA.
- affine variational inequality
- global error bound
- global linear convergence