SIAM Journal on Scientific and Statistical Computing
Normal maps inducted by linear transformations
Mathematics of Operations Research
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
A semismooth equation approach to the solution of nonlinear complementarity problems
Mathematical Programming: Series A and B
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
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We consider a class of complementarity problems involving functions which are not Lipschitz continuous. In this paper we reformulate this class of non-Lipschitzian complementarity problems into a Lipschitzian complementarity problem. Then we propose an inexact smoothing Newton method to solve this Lipschitzian complementarity problem. We prove that our proposed method converges quadratically and globally under a mild condition. Numerical results show that this method is promising. This method can solve these kinds of complementarity problems with one million variables in reasonable time on a PC with 1 GB of RAM.