Convergence rate estimates for Tikhonov’s scheme as applied to ill-posed nonconvex optimization problems

Abstract

We examine the convergence rate of approximations generated by Tikhonov’s scheme as applied to ill-posed constrained optimization problems with general smooth functionals on a convex closed subset of a Hilbert space. Assuming that the solution satisfies a source condition involving the second derivative of the cost functional and depending on the form of constraints, we establish the convergence rate of the Tikhonov approximations in the cases of exact and approximately specified functionals.