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An algorithm for generalized variational inequality with pseudomonotone mapping. (English) Zbl 1208.65092
A projection algorithm for approximating solutions $x^*\in C$ (with $\xi\in F(x^*)$) of a variational inequality $\langle\xi,y-x^*\rangle\geq 0, y\in C$ is proposed, where $F$ is a continuous and pseudomonotone multi-valued mapping from $C$ into ${\mathbb{R}}^n$ with nonempty compact convex values and $C\subseteq {\mathbb{R}}^n$ is closed and convex. The authors prove convergence of the algorithm and derive a convergence rate result under additional assumptions on $F$ and on the solutions set.

##### MSC:
 65K15 Numerical methods for variational inequalities and related problems 49J40 Variational methods including variational inequalities 49M25 Discrete approximations in calculus of variations
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##### References:
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