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Zbl 0933.65076
Noor, Muhammad Aslam; Rassias, Themistocles M.
Projection methods for monotone variational inequalities.
(English)
[J] J. Math. Anal. Appl. 237, No.2, 405-412 (1999). ISSN 0022-247X

The authors give some new iterative methods for solving monotone variational inequalities of the form $$\langle Tu,v- u\rangle\ge 0,\ \forall v\in K,$$ where $K$ is a closed convex set in a Hilbert space $H$, $T: K\to H$ is a nonlinear operator. The convergence of the given methods requires the monotonicity and pseudomonotonicity of the operator $T$, whereas the convergence of known methods requires the Lipschitz continuity of the monotone operator $T$.\par No numerical tests for the given methods are presented.
[H.Benker (Merseburg)]
MSC 2000:
*65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities
49M15 Methods of Newton-Raphson, Galerkin and Ritz types

Keywords: projection methods; monotone variational inequalities; Hilbert space; nonlinear operator; convergence

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