# A class of projection and contraction methods for monotone variational inequalities

A class of projection and contraction methods for monotone variational inequalities In this paper we introduce a new class of iterative methods for solving the monotone variational inequalities $$u* \in \Omega , (u - u*)^T F(u*) \geqslant 0, \forall u \in \Omega .$$ Each iteration of the methods presented consists essentially only of the computation of F ( u ), a projection to Ω, v := P Ω ( u - F ( u )), and the mapping F ( v ). The distance of the iterates to the solution set monotonically converges to zero. Both the methods and the convergence proof are quite simple. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# A class of projection and contraction methods for monotone variational inequalities

, Volume 35 (1) – Jan 1, 1997
8 pages

/lp/springer_journal/a-class-of-projection-and-contraction-methods-for-monotone-variational-HVXt0tx9uN
Publisher
Springer-Verlag
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683320
Publisher site
See Article on Publisher Site

### Abstract

In this paper we introduce a new class of iterative methods for solving the monotone variational inequalities $$u* \in \Omega , (u - u*)^T F(u*) \geqslant 0, \forall u \in \Omega .$$ Each iteration of the methods presented consists essentially only of the computation of F ( u ), a projection to Ω, v := P Ω ( u - F ( u )), and the mapping F ( v ). The distance of the iterates to the solution set monotonically converges to zero. Both the methods and the convergence proof are quite simple.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jan 1, 1997

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