On a regularized variant of the two-step projection-gradient method

A regularization method based on the two-step projection-gradient method along with the penalty function method is suggested for solving the minimization problem with incorrectly given assumed data. The sufficient conditions of convergence are presented. A minimization problem is considered with a given convex closed set from some Hilbert space H and some functions defined and Fresche differentiable over H. The problem is unstable to disturbances of the assumed data and it should be solved using the regularization methods.