About a regularized method for solving a constrained pseudoinverse problem

For a constrained pseudoinverse problem with operators satisfying complementarity condition we suggest a one-parametric continuous method of regularization of second order. This method is based on stabilization of solutions to Cauchy problems for linear differential equation of second order in Hilbert space constructed on the base of the method of a heavy globule. We establish conditions on the parametric function of regularization and levels of disturbances ensuring the stability of the method in the class of all constrained disturbances.