在過去二十年中，數學家發展了很多的方法來處理非線性互補問題。其中最有名的是轉換成解一個非線性方程組或是最小值問題。在這篇論文中，我們研究一個新函數。特別的是，我們列出這個函數有全面誤差估計的條件和有有界階段集的條件。

[1] B. Chen, X. Chen, and C. Kanzow, A Penalized Fischer-Burmeister NCP-
function: Theoretical Investigation and Numerical Results, Mathematical Program-
ming, vol. 88, pp. 211-216, 2000.

[2] J.-S. Chen, The Semismooth-related Properties of a Merit function and a Descent
Method for the Nonlinear Complementarity Problem, Journal of Global Optimization,
vol. 24, pp. 565-580, 2006.

[3] J.-S. Chen, On Some NCP-functions Based on the Generalized Fischer-Burmeister
function, Asia-Paci¯c Journal of Opertional Research, vol. 24, pp. 401-420, 2007.

[4] J.-S. Chen and S. Pan, A Family of NCP-functions and a Descent Method for
the Nonlinear Complementarity Problem, to appear in Computational Optimization
and Applications, 2008.

[5] J.-S. Chen and S. Pan, A Family of Penalized NCP-functions Based on the Gen-
eralized Fischer-Burmeister Functions: Theoretical Investigation and Numerical Re-
sults, submitted manuscript, 2007.

[6] R.W. Cottle, J.-S. Pang and R.-E. Stone, The Linear Complementarity Prob-
lem, Academic Press, New York, 1992.

[7] S. Dafermos, An Iterative Scheme for Variational Inequalities, Mathematical Pro-
gramming, vol. 26, pp.40-47, 1983.

[8] F. Facchinei and J. Soares, A New Merit Function for Nonlinear Complemen-
tarity Problems and a Related Algorithm, SIAM Journal on Optimization, vol. 7, pp.
225-247, 1997.

[9] A. Fischer, A Special Newton-type Optimization Method, Optimization, vol. 24,
pp. 269-284, 1992.

[10] M. Fukushima Merit Functions for Varitional Inequality and Complementarity
Problem, Nonlinear Optimization and Applications, edited by G Di Pillo and F.
Giannessi, Pleneum Press, New York, pp. 155-170, 1996.

[11] C. Geiger and C. Kanzow, On the Resolution of Monotone Complementarity
Problems, Computational Optimization and Applications, vol. 5, pp. 155-173, 1996.

[12] P. T. Harker and J.-S. Pang, Finite Dimensional Variational Inequality and
Nonlinear Complementarity Problem: A Survey of Theory, Algorithms and Applica-
tions, Mathematical Programming, vol. 48, pp. 161-220, 1990.

[13] H. Jiang, Unconstrained Minimization Approaches to Nonlinear Complementarity
Problems, Journal of Global Optimization, vol. 9, pp. 169-181, 1996.

[14] C. Kanzow, Nonlinear Complementarity as Unconstrained Optimization, Journal
of Optimization Theory and Applications, vol. 88, pp. 139-155, 1996.

[15] C. Kanzow and N. Yamashita and M. Fukushima, New NCP-functions and
Their Properties, Journal of Optimization Theory and Applications, vol. 94, pp.
115-135, 1997.

[16] O. L. Mangasarian, Equivalence of the Complementarity Problem to a System
of Nonlinear Equations, SIAM Journal on Applied Mathematics, vol. 31, pp. 89-92,
1976.

[17] J.-S. Pang, A Posteriori Error Bounds for the Linearly-constrained Variational
Inequality Problem, Mathematics of Operations Research, vol. 12, pp. 474-484, 1987.

[18] J.-S. Pang, Complementarity problems, Handbook of Global Optimization, edited
by R. Horst and P. Pardalos, Kluwer Academic Publishers, Boston, Massachusetts,
pp. 271-338, 1994.

[19] J.-S. Pang, Newton's Method for B-di®erentiable Equations, Mathematics of Op-
erations Research, vol. 15, pp. 311-341, 1990.

[20] J.-S. Pang and D. Chan, Iterative Methods for Variational and Complemantarity
Problems, Mathematics Programming, vol. 27, 99. 284-313, 1982.

[21] P. Tseng, Growth Behavior of a Class of Merit Functions for the Nonlinear Com-
plementarity Problem, Journal of Optimization Theory and Applications, vol. 89, pp.
17-37, 1996.

[22] N. Yamashita and M. Fukushima, On Stationary Points of the Implicit La-
grangian for the Nonlinear Complementarity Problems, Journal of Optimization The-
ory and Applications, vol. 84, pp. 653-663, 1995.

[23] N. Yamashita and M. Fukushima, Modi¯ed Newton Methods for Solving a
Semismooth Reformulation of Monotone Complementarity Problems, Mathematical
Programming, vol. 76, pp. 469-491, 1997.

[24] K. Yamada, N. Yamashita, and M. Fukushima, A New Derivative-free De-
scent Method for the Nonlinear Complementarity Problems, in Nonlinear Optimiza-
tion and Related Topics edited by G.D. Pillo and F. Giannessi, Kluwer Academic
Publishers, Netherlands, pp. 463-487, 2000.