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Projection methods for monotone variational inequalities. (English) Zbl 0933.65076
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 $T$. No numerical tests for the given methods are presented.

65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
49M15Newton-type methods in calculus of variations
Full Text: DOI
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