Regularized continuous linearization method of the second order for the minimization problems with inexact initial data

The minimization problem is considered when a convex closed set from some Hilbert space H is given and the functions are defined and Fresche differentiable over H. The problem is unstable to disturbances of initial data and the regularization methods should be applied to solving the problem. A regularization method based on the continuous variant of a linearization method of the second order is proposed and studied. It is assumed that instead of exact values of the functions and their gradients, the approximate values are known.