  We consider choice of the regularization parameter in Tikhonov method in the
case of the unknown noise level of the data. From known heuristic parameter
choice rules often the best results were obtained in the quasi-optimality
criterion where the parameter is chosen as the global minimizer of the
quasi-optimality function. In some problems this rule fails, the error of the
Tikhonov approximation is very large. We prove, that one of the local
minimizers of the quasi-optimality function is always a good regularization
parameter. We propose an algorithm for finding a proper local minimizer of the
quasi-optimality function.
