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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 $(x-x^*)^T(Hx^*+C)\ge0,\,\forall x\in\Omega$ 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.

65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
Full Text: DOI
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