Quasi-newton Methods for Convex Constrained Nonlinear Systems and Their Application

We address the solution of convex constrained nonlinear systems by new linesearch Quasi-Newton methods. These methods are based on a proper use of the projection map onto the constraint set and on a derivativefree and nonmonotone linesearch strategy. The convergence properties of the proposed methods are presented along with a worst-case iteration complexity bound. Several implementations of the proposed scheme are discussed and validated on bound-constrained problems including gas distribution network models. The results reported show that the new methods are very efficient and competitive with an existing affine-scaling procedure.