VARIATIONAL INEQUALITIES GOVERNED BY BOUNDEDLY LIPSCHITZIAN AND STRONGLY MONOTONE OPERATORS
Songnian He, Hong‐Kun Xu · 2009
Consider the variational inequality V I(C,F) of finding a point x 2 C satisfying the property hFx ,x x i 0 for all x 2 C, where C is a nonempty closed convex subset of a real Hilbert space H and F : C ! H is a nonlinear mapping. If F is boundedly Lipschitzian and strongly monotone, then we prove that V I(C,F) has a unique solution and iterative algorithms can be devised to approximate this solution. In the case where C is the set of fixed points of a nonexpansie mapping, we also invent a hybrid iterative algorithm to