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Zbl 1037.65066
Liao, Li-Zhi; Wang, Shengli
A self-adaptive projection and contraction method for monotone symmetric linear variational inequalities.
(English)
[J] Comput. Math. Appl. 43, No. 1-2, 41-48 (2002). ISSN 0898-1221

A modification of projection methods in finite dimensional spaces for symmetric variational inequalities of type $(x-x^*)^T(Hx^*+C)\ge0,\,\forall x\in\Omega$ 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.
[Christian Grossmann (Dresden)]
MSC 2000:
*65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities

Keywords: symmetric variational inequality; projection method; contraction method; adaptive parameters; projection methods; numerical examples

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