## On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization

We propose a new termination criteria suitable for potentially singular, zero or non-zero residual, least-squares problems, with which cubic regularization variants take at most $\mathcal{O}(\epsilon^{-3/2})$ residual- and Jacobian-evaluations to drive either the Euclidean norm of the residual or its gradient below $\epsilon$; this is the best-known bound for potentially singular nonlinear least-squares problems. We then … Read more