Regularization of Nonlinear Ill-Posed Variational Inequalities and Convergence Rates

摘要: Let H be a Hilbert space and K nonempty closed convex subset of H. For f ∈ H, we consider the (ill-posed) problem finding u for which ≥ 0 all v K, where A : → is monotone (not necessarily linear) operator. We study approximation solutions variational inequality by using following perturbed inequality: fδ ‖ − ≤ δ, find ueδ, η Kη Kη, e, are positive parameters, perturbation set in establish convergence rate O(e1 / 3) regularized inequalities to solution original Mosco sets, weakly differentiable inverse-strongly-monotone