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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 ${\left(x-{x}^{*}\right)}^{T}\left(H{x}^{*}+C\right)\ge 0,\phantom{\rule{0.166667em}{0ex}}\forall x\in {\Omega }$ with nonempty closed convex set ${\Omega }$ is considered. A known iterative method which bases on an equivalent fixed point formulation $x={P}_{{\Omega }}\left(x-\beta \left(Hx+c\right)\right)$ 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 Optimization techniques (numerical methods) 49J40 Variational methods including variational inequalities