Convergence of the Gauss-Newton method for convex composite optimization under a majorant condition

TL;DR

This paper introduces a new semi-local convergence analysis for an extended Gauss-Newton method applied to convex composite optimization, utilizing a majorant condition to simplify convergence proofs and define well-behaved regions.

Contribution

It provides a novel convergence analysis framework for the Gauss-Newton method under a majorant condition, expanding understanding of its behavior in convex composite problems.

Findings

Convergence is guaranteed under quasi-regular initial points.

The majorant condition simplifies the convergence proof.

Defined regions where the Gauss-Newton sequence behaves well.

Abstract

Under the hypothesis that an initial point is a quasi-regular point, we use a majorant condition to present a new semi-local convergence analysis of an extension of the Gauss-Newton method for solving convex composite optimization problems. In this analysis the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where a Gauss-Newton sequence is "well behaved".