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 \(u^*\in\Omega\), \((u-u^*)^Tf(u^*)\geq 0\), \(\forall u\in\Omega\). 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.
MSC:
| 90C30 | Nonlinear programming |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 65K05 | Numerical mathematical programming methods |
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