On the convergence of an inexact Gauss–Newton trust‐region method for nonlinear least‐squares problems with simple bounds

We introduce an inexact Gauss–Newton trust‐region method for solving bound‐constrained nonlinear least‐squares problems where, at each iteration, a trust‐region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties. Some numerical illustration is also presented.