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A class of projection and contraction methods for monotone variational inequalities. (English) Zbl 0865.90119
Summary: We introduce a new class of iterative methods for solving the monotone variational inequalities $u^*\in\Omega$, $(u-u^*)^Tf(u^*)\ge 0$, $\forall u\in\Omega$. Each iteration of the methods consists essentially only of the computation of $F(u)$, a projection to $\Omega$, $v:=P_\Omega[u-F(u)]$, and the mapping $F(v)$. The distance of the iterates to the solution set monotonically converges to zero. Both the methods and the convergence proof are quite simple.

90C30Nonlinear programming
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
65K05Mathematical programming (numerical methods)
Full Text: DOI
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