Expanding the Applicability of the Gauss-Newton Method for Convex Optimization under a Regularity Condition

摘要

A new semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems is presented using the concept of quasi-regularity for an initial point. The convergence analysis is based on a combination of a center-majorant and majorant function. The results extend the applicability of the Gauss-Newton method under the same computational cost as in earlier studies such as. In particular, the new convergence criteria are weaker; the error estimates on the distance involved are tighter and the information on the location of the solution is at least as precise.