A regularized method for solving constrained pseudoinverse problems

For a constrained pseudoinverse problem whose operators satisfy the complementarity condition we propose a one-parameter continuous regularization method of the second order. This method is based on stabilization of solutions to Cauchy problems for a linear differential equation of the second order in a Hilbert space which is obtained from the heavy ball method. We establish requirements to the parametric regularization function and perturbation levels that ensure the stability of the method in the class of all possible bounded perturbations.