Solving Nonlinear Systems Of Equations By Means Of Quasi-Newton Methods With A Nonmonotone Strategy

A nonmonotone strategy for solving nonlinear systems of equations is introduced. The idea consists of combining efficient local methods with an algorithm that reduces monotonically the squared norm of the system in a proper way. The local methods used are Newton's method and two quasiNewton algorithms. Global iterations are based on recently introduced boxconstrained minimization algorithms. We present numerical experiments. 1 INTRODUCTION Given F : IR n ! IR n ; F = (f 1 ; : : : ; f n ) T , our aim is to find solutions of F (x) = 0: (1) We assume that F is well defined and has continuous partial derivatives on an open set of IR n . J(x) denotes the Jacobian matrix of partial derivatives of F (x). We are mostly interested in problems where n is large and J(x) is structurally sparse. This means that most entries of J(x) are zero for all x in the domain of F . The package Nightingale has been developed at the Department of Applied Mathematics of the University of Campinas for..