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A self-adaptive projection and contraction method for monotone symmetric linear variational inequalities. (English) Zbl 1037.65066

A modification of projection methods in finite dimensional spaces for symmetric variational inequalities of type \((x-x^*)^T(Hx^*+C)\geq0,\,\forall x\in\Omega\) with nonempty closed convex set \(\Omega\) is considered. A known iterative method which bases on an equivalent fixed point formulation \(x=P_\Omega(x-\beta(Hx+c))\) is modified by replacing the constant \(\beta>0\) by parameters \(\beta_k\) which are adapted to the iterates \(x^k\). A convergence theorem is established and numerical examples are given. However, in the experiments the earlier restrictions for the choice of \(\beta_k\) are relaxed.

MSC:

65K10 Numerical optimization and variational techniques
49J40 Variational inequalities
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