Tikhonov-regularization of ill-posed linear operator equations on closed convex sets

AbstractIn this paper we derive conditions under which the constrained Tikhonov-regularized solutions xα,c of an ill-posed linear operator equation Tx = y (i.e., xα,c is the minimizing element of the functional ∥Tx − y∥2 + α ∥x∥2 in the closed convex set C) converge to the best-approximate solution of the equation in C with rates o(α12) and O(α), respectively