Extending the applicability of the Gauss–Newton method for convex composite optimization using restricted convergence domains and average Lipschitz conditions

Abstract

We present a new technique to study the semilocal convergence analysis of the Gauss–Newton method (GNA) to solve convex composite optimization problems under average-type Lipschitz conditions. The novelty of this technique lies in the fact that tighter majorizing sequences than in earlier studies can be obtained. This is achieved by restricting the domain where the iterates of GNA lie. Special cases and numerical examples are also provided in this study. © 2016, Sociedad Española de Matemática Aplicada.