Clustering Effect for Stationary Points of Discrepancy Functionals Associated with Conditionally Well-Posed Inverse Problems

Abstract

In a Hilbert space we consider a class of conditionally well-posed inverse problems for which a Holder-type estimate of conditional stability on a closed convex bounded subset holds. We investigate the Ivanov quasi-solution method and its finite-dimensional version associated with minimization of a multi-extremal discrepancy functional over a conditional stability set or over a finite-dimensional section of this set, respectively. For these optimization problems, we prove that each of their stationary points that is located not too far from the desired solution of the original inverse problem belongs to a small neighborhood of the solution. Estimates for the diameter of this neighborhood in terms of error levels in input data are also given.