Some general conditions for regularization of ill-posed variational problems

V. A. Morozov

Lomonosov Moscow State University, Research Computing Center

Abstract: Some aspects of stable solving a rather wide class of ill-posed variational problems (generalized minimization) are considered. We indicate the conditions that ensure the convergence of regularization, residual, and quasisolution methods in the original space as well as the strong convergence under certain additional conditions imposed on functionals. Our results substantially generalize a number of results obtained earlier for linear and nonlinear equations with unbounded operators. The influence of errors in the given and stabilizing functionals is studied. The work was supported by the Russian Foundation for Basic Research (04-01-00026, 03-01-96698).

Keywords: ill-posed variational problems, generalized minimization, residual method, linear operator equations, inverse problems, stable methods.

UDC: 519.2:541.1