  This works aims at understanding further convergence properties of first
order local search methods with complex geometries. We focus on the composite
optimization model which unifies within a simple formalism many problems of
this type. We provide a general convergence analysis of the composite
Gauss-Newton method under tameness assumptions (an extension of
semi-algebraicity). Tameness is a very general condition satisfied by virtually
all problems solved in practice. The analysis is based on recent progresses in
understanding convergence properties of sequential convex programming methods
through the value function.
