On stationary points of the implicit Lagrangian for nonlinear complementarity problems
Journal of Optimization Theory and Applications
Growth behavior of a class of merit functions for the nonlinear complementarity problem
Journal of Optimization Theory and Applications
On the resolution of monotone complementarity problems
Computational Optimization and Applications
Nonlinear complementarity as unconstrained optimization
Journal of Optimization Theory and Applications
Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Solution of monotone complementarity problems with locally Lipschitzian functions
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
A Comparison of Large Scale Mixed Complementarity Problem Solvers
Computational Optimization and Applications
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
A smoothing Newton method for general nonlinear complementarity problems
Computational Optimization and Applications - Special issue on nonsmooth and smoothing methods
A New Merit Function For Nonlinear Complementarity Problems And A Related Algorithm
SIAM Journal on Optimization
Journal of Global Optimization
Complementarity: Applications, Algorithms and Extensions (Applied Optimization)
Complementarity: Applications, Algorithms and Extensions (Applied Optimization)
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Information Sciences: an International Journal
Numerical comparisons of two effective methods for mixed complementarity problems
Journal of Computational and Applied Mathematics
Nonlinear complementarity problem and solution methods
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part I
A nonsmooth algorithm for cone-constrained eigenvalue problems
Computational Optimization and Applications
A new class of penalized NCP-functions and its properties
Computational Optimization and Applications
A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P0-function
Journal of Global Optimization
Neural networks for solving second-order cone constrained variational inequality problem
Computational Optimization and Applications
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In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization involving an NCP function. In this paper, we propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+驴), and show several favorable properties of the proposed functions. In addition, we also propose a descent algorithm that is indeed derivative-free for solving the unconstrained minimization based on the merit functions from the proposed NCP functions. Numerical results for the test problems from MCPLIB indicate that the descent algorithm has better performance when the parameter p decreases in (1,+驴). This implies that the merit functions associated with p驴(1,2), for example p=1.5, are more effective in numerical computations than the Fischer-Burmeister merit function, which exactly corresponds to p=2.