Local convergence of the Gauss–Newton methods for constrained nonlinear equations

We derive, from unified principles, local convergence and rate-of-convergence results for the classical Gauss-Newton method in a variety of settings. These include overdetermined and underdetermined systems of equations, constrained and unconstrained, possibly with inexact solution of subproblems, as well as the projected variant in the constrained case. Moreover, by a counter-example we show that contrary to some results claimed in the literature, the projected Gauss-Newton method in general does not converge superlinearly under any reasonable assumptions. We then establish its linear rate of convergence.