The use of unsmooth penalty functions in the regularization of unstable minimization problems

Unstable minimization problems with approximate initial data are solved by a method of regularization in which the penalty functions are obtained by smoothing of unsmooth functions of the ‘cut’ type. Matching conditions for the parameters of the method are found so that convergence is obtained with a finite value of the penalty coefficient, a regularizing operator is constructed, and estimates are obtained for the rate of convergence with respect to the function and the argument.