A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
A non-interior-point continuation method for linear complementarity problems
SIAM Journal on Matrix Analysis and Applications
A class of smoothing functions for nonlinear and mixed complementarity problems
Computational Optimization and Applications
Some Noninterior Continuation Methods for LinearComplementarity Problems
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP
Mathematical Programming: Series A and B
A smoothing-type algorithm for solving system of inequalities
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Smoothing algorithms for complementarity problems over symmetric cones
Computational Optimization and Applications
A monotone semismooth Newton type method for a class of complementarity problems
Journal of Computational and Applied Mathematics
SIAM Journal on Optimization
A non-interior continuation algorithm for the CP based on a generalized smoothing function
Journal of Computational and Applied Mathematics
A fixed-point method for a class of super-large scale nonlinear complementarity problems
Computers & Mathematics with Applications
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In this paper, we investigate a class of nonlinear complementarity problems arising from the discretization of the free boundary problem, which was recently studied by Sun and Zeng [Z. Sun, J. Zeng, A monotone semismooth Newton type method for a class of complementarity problems, J. Comput. Appl. Math. 235 (5) (2011) 1261-1274]. We propose a new non-interior continuation algorithm for solving this class of problems, where the full-Newton step is used in each iteration. We show that the algorithm is globally convergent, where the iteration sequence of the variable converges monotonically. We also prove that the algorithm is globally linearly and locally superlinearly convergent without any additional assumption, and locally quadratically convergent under suitable assumptions. The preliminary numerical results demonstrate the effectiveness of the proposed algorithm.