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Convergence properties of projection and contraction methods for variational inequality problems. (English) Zbl 0980.90093
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.

90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
90C30Nonlinear programming
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