On Affine Scaling Inexact Dogleg Methods for Bound-constrained Nonlinear Systems on Affine Scaling Inexact Dogleg Methods for Bound-constrained Nonlinear Systems *

A class of trust-region methods for large scale bound-constrained systems of nonlinear equations is presented. The methods in this class follow the so called affine-scaling approach and can efficiently handle large scale problems. At each iteration, a suitably scaled region around the current approximate solution is defined and, within such a region, the norm of the linear model of F is trusted to be an adequate representation of the merit function ∥F∥. Both spherical and elliptical trust-regions are allowed. An inexact dogleg method is used to obtain an approximate minimizer of the linear model within the trust-region and the feasible set Ω. Thus, strictly feasible iterates are formed and a strictly feasible approximation of the solution is ensured. Global convergence results are established without any Lipschitz assumption on F ′(x) and locally fast convergence is showed under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds. In fact, a rather general class of scaling matrices is allowed in actual algorithms. An algorithm based on the standard spherical trust-region and the pioneer scaling matrix given by Coleman and Li is implemented in a Matlab code and its numerical performance is shown.