NCP Functions Applied to Lagrangian Globalization for the Nonlinear Complementarity Problem
Journal of Global Optimization
Lagrangian globalization methods for nonlinear complementarity problems
Journal of Optimization Theory and Applications
A Smoothing Newton Method for General Nonlinear Complementarity Problems
Computational Optimization and Applications
Quadratic one-step smoothing Newton method for P0-LCP without strict complementarity
Applied Mathematics and Computation
An iterative method for solving semismooth equations
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
Applications of smoothing methods in numerical analysis and optimization
Focus on computational neurobiology
A Smoothing Newton Method for Semi-Infinite Programming
Journal of Global Optimization
A matrix-splitting method for symmetric affine second-order cone complementarity problems
Journal of Computational and Applied Mathematics
A new smoothing quasi-Newton method for nonlinear complementarity problems
Journal of Computational and Applied Mathematics
A smoothing Newton-type method for generalized nonlinear complementarity problem
Journal of Computational and Applied Mathematics
Globally convergent Jacobian smoothing inexact Newton methods for NCP
Computational Optimization and Applications
A nonmonotone smoothing Newton algorithm for solving nonlinear complementarity problems
Optimization Methods & Software
A matrix-splitting method for symmetric affine second-order cone complementarity problems
Journal of Computational and Applied Mathematics
Smoothing Newton method for NCP with the identification of degenerate indices
Journal of Computational and Applied Mathematics
A new hybrid method for nonlinear complementarity problems
Computational Optimization and Applications
A smoothing Broyden-like method for the mixed complementarity problems
Mathematical and Computer Modelling: An International Journal
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We present a new algorithm for the solution of general (not necessarily monotone) complementarity problems. The algorithm is based on a reformulation of the complementarity problem as a nonsmooth system of equations by using the Fischer--Burmeister function. We use an idea by Chen, Qi, and Sun and apply a Jacobian smoothing method (which combines nonsmooth Newton and smoothing methods) to solve this system. In contrast to that of Chen, Qi, and Sun, however, our method is at least well defined for general complementarity problems. Extensive numerical results indicate that the new algorithm works very well. In particular, it can solve all nonlinear complementarity problems from the MCPLIB and GAMSLIB libraries.