On the regularized Lagrange principle in iterative form and its application for solving unstable problems

Abstract

For a convex programming problem in a Hilbert space with operator equality constraints, the Lagrange principle in sequential nondifferential form or, in other words, the regularized Lagrange principle in iterative form, that is resistant to input data errors is proved. The possibility of its applicability for direct solving unstable inverse problems is discussed. As an example of such problem, we consider the problem of finding the normal solution of the Fredholm integral equation of the first kind. The results of the numerical calculations are shown.