Modified Projection-Type Methods for Monotone Variational Inequalities

Authors:
Michael V. Solodov;Paul Tseng
Affiliations:
-;-
Venue:
SIAM Journal on Control and Optimization
Year:
1996

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Abstract

We propose new methods for solving the variational inequality problem where the underlying function $F$ is monotone. These methods may be viewed as projection-type methods in which the projection direction is modified by a strongly monotone mapping of the form $I - \alpha F$ or, if $F$ is affine with underlying matrix $M$, of the form $I+ \alpha M^T$, with $\alpha \in (0,\infty)$. We show that these methods are globally convergent, and if in addition a certain error bound based on the natural residual holds locally, the convergence is linear. Computational experience with the new methods is also reported.