Algorithms for Nonlinear Least-squares Problems

This paper addresses the nonlinear least-squares problem which arises most often in data fitting applications. Much research has focused on the development of specialized algorithms that attempt to exploit the structure of the nonlinear least-squares objective. The author surveys numerical methods developed for problems in which sparsity in the derivatives of f is not taken into account in formulating algorithms. Keywords: Multivariate functions; Gauss-Newton methods; Levenberg Marquardt methods; Quasi-Newton methods; Quadratic programming; Unconstrained optimization methods. (KR).