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A new method for a class of linear variational inequalities. (English) Zbl 0813.49009
The author considers a class of linear variational inequalities of the form \[ u\in \Omega(\nu- u)^ T (Mu+ q)\geq 0,\quad\text{for all }\nu\in \Omega, \] where \(M\) is a positive semidefinite matrix, \(q\in \mathbb{R}^ n\) and \(\Omega\subset \mathbb{R}^ n\) is a closed convex set. A new iteration scheme for the numerical solution of this problem is given. Each iteration of this method consists only of a projection to a convex set and two matrix-vector multiplications.

MSC:
49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K10 Numerical optimization and variational techniques
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