On affine-scaling inexact dogleg methods for bound-constrained nonlinear systems

Abstract

Within the framework of affine-scaling trust-region methods for bound-constrained problems, we discuss the use of an inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Then, we focus on large-scale bound-constrained systems of nonlinear equations which often arise in practical applications when some of the unknowns are naturally subject to constraints due to physical arguments. We introduce an inexact affine-scaling method for such a class of problems that employs the inexact dogleg procedure. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix that is used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given.