Expanding the applicability of the gauss-newton method for convex optimization under restricted convergence domains and majorant conditions

Capítulo del libro "Iterative Methods and Their Dynamics with Applications"n this chapter we are concerned with the convex composite optimizations problem. This work is mainly motivated by the work in [17,23].We present a convergence analysis of Gauss-Newton method (defined by Algorithm (GNA) in Sec. 20.2). The convergence of GNA is based on the majorant function in [17] (to be precised in Sec. 20.2). They follow the same formulation using the majorant function provided in [23] (see [21,23,28,29]). In [3,5,8], a convergence analysis in a Banach space setting was given for (GNM) defined (formula presented)