On the convergence analysis of the nonlinear ABS methods (Q1261760)

In order to complete the convergence theory of nonlinear ABS algorithm, through a careful investigation to the algorithm structure, the author converts the nonlinear ABS algorithm into an inexact Newton method. Based on such equivalent variation, the Kantorovich type convergence of the ABS algorithm is established and the convergence conditions of the algorithm that only depend on initial conditions are obtained, which provides a useful basis for the choice of the initial point of the ABS algorithm.