## A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems (1997)

Citations: | 29 - 4 self |

### BibTeX

@MISC{Facchinei97anonsmooth,

author = {Francisco Facchinei and Christian Kanzow},

title = {A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems},

year = {1997}

}

### OpenURL

### Abstract

A new algorithm for the solution of large-scale nonlinear complementarity problems is introduced. The algorithm is based on a nonsmooth equation reformulation of the complementarity problem and on an inexact Levenberg-Marquardt-type algorithm for its solution. Under mild assumptions, and requiring only the approximate solution of a linear system at each iteration, the algorithm is shown to be both globally and superlinearly convergent, even on degenerate problems. Numerical results for problems with up to 10000 variables are presented. 1 Introduction We consider the complementarity problem NCP(F ), which is to find a vector in IR n satisfying the conditions x 0; F (x) 0; x T F (x) = 0; where F : IR n ! IR n is a continuously differentiable function. Nonlinear complementarity problems have important applications, see, e.g., [11,19], which often call for the solution of large-scale problems. During the last few years many methods have been developed for the solution of the non...