An Adaptive Nonmonotone Trust Region Method Based on a Structured Quasi Newton Equation for the Nonlinear Least Squares Problem

In this work an iterative method to solve the nonlinear least squares problem is presented. The algorithm combines a secant method with a strategy of nonmonotone trust region. In order to dene the quadratic model, the Hessian matrix is chosen using a secant approach that takes advantage of the structure of the problem, and the radius of the trust region is updated following an adaptive technique. Moreover, convergence properties of this algorithm are proved. The numerical experimentation, in which several ways of choosing the Hessian matrix are compared, shows the effiency and robustness of the method.Sociedad Argentina de Informática e Investigación Operativ