Convergence and evaluation-complexity analysis of a regularized tensor-Newton method for solving nonlinear least-squares problems

摘要

Given a twice-continuously differentiable vector-valued function r(x), a local minimizer of r(x)2 is sought. We propose and analyse tensor-Newton methods, in which r(x) is replaced locally by its second-order Taylor approximation. Convergence is controlled by regularization of various orders. We establish global convergence to a first-order critical point of r(x)2, and provide function evaluation bounds that agree with the best-known bounds for methods using second derivatives. Numerical experiments comparing tensor-Newton methods with regularized Gauss-Newton and Newton methods demonstrate the practical performance of the newly proposed method.