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A relaxed projection method for variational inequalities. (English) Zbl 0598.49024
Let K be a closed convex set in \(R^ n\), f a mapping from \(R^ n\) into itself, then consider the problem of finding \(u\in K\) such that (*) (f(u),v-u)\(\geq 0\), for all \(v\in K\). It is well known that the projection methods can be used to find the approximate solution of (*) numerically. In this paper, the author presents a modification. In the proposed modified algorithm, each iteration consists of a projection onto a half space containing the given closed set rather the latter set itself, which makes the implementation of the algorithm easy as compared to the standard projection methods. Convergence criteria are also discussed along with some examples.
Reviewer: M.A.Noor

MSC:
49M20 Numerical methods of relaxation type
49J40 Variational inequalities
65K10 Numerical optimization and variational techniques
47H05 Monotone operators and generalizations
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