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Zbl 0980.90093
Xiu, N.; Wang, C.; Zhang, J.
Convergence properties of projection and contraction methods for variational inequality problems.
(English)
[J] Appl. Math. Optimization 43, No.2, 147-168 (2001). ISSN 0095-4616; ISSN 1432-0606/e

Some convergence properties of the projection and contraction method are proven in solving the variational inequality problem of finding a vector $x^*$ of a convex closed set $K\subseteq \bbfR^n$ such that $\langle f(x^*), x-x^* \rangle\ge 0$ for all $x\in K$, where $f$ is a continuous vector function from $R^n$ to itself. In one of the variants of the method, when a nondegenerate solution is obtained, the entire optimal face can be identified after a finite number of iterations.
[Dinh The Luc (Avignon)]
MSC 2000:
*90C33 Complementarity problems
90C30 Nonlinear programming

Keywords: convergence; projection; contraction; variational inequality problem

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