Expanding the applicability of the Gauss-Newton method for convex optimization under a regularity condition (Q2927782)

The authors present a new semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems using the concept of quasi-regularity for an initial point. Using a combination of a majorant and a center majorant function which is a special case of the majorant function and a more precise function to use than the majorant function for the computation of the upper bounds of the norms of the inverse involved, they present a semilocal convergence analysis with the advantages: tighter error estimates on the distances involved and the information on the location of the solution is at least as precise. These advantages are obtained under the same computational cost using the same or weaker sufficient convergence hypotheses. The authors expand the applicability of the Gauss-Newton algorithm under the Robinson condition in order to approximate a solution of a convex composite optimization problem.