我們提出廣義FB函數的一個平滑逼近，這裡的廣義FB函數將二次範數的FB函數推廣成p次範數(p大於1)，而且建立一些適合的性質。運用平滑函數，我們將混合型互補問題轉化成解一系列的方程式。

We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and
establish some favorable properties for it, for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into
solving a sequence of smooth system of equations.

[1] S. C. Billups, S. P. Dirkse and M. C. Soares, A comparison of algorithms
for large scale mixed complementarity problems, Computational Optimization and
Applications, vol. 7, pp. 3{25, 1997.
[2] S. C. Billups, and M. C. Soares, QPCOMP: A quadratic programming based
solver for mixed complementarity problems, Mathematical Programming, vol. 76, pp.
533{562, 1997.
[3] B. Chen and P. T. Harker, A non-intertior-point continuation method for linear
complementarity problem, SIAM Journal on Matrix Analysis and Applications, vol.
14, pp. 1168{1190, 1993.
[4] C. Chen and O. L. Mangasarian, A class of smoothing functions for nonlinear
and mixed complementarity problems, Computational Optimization and Applications,
vol. 5, pp. 97{138, 1995.
[5] 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. 36, pp. 565{580, 2006.
[6] 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.
[7] J.-S. Chen and S. Pan, A family of NCP-functions and a descent method for the
nonlinear complementarity problem, Computational Optimization and Applications,
vol. 40, pp. 389{404, 2008.
[8] F. H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
[9] X. Chen and L. Qi, A parameterized Newton method and a Broyden-like method
for solving nonsmooth equations, Computational Optimization and Applications, vol.
3, pp. 157{179, 1994.
[10] X. Chen, L. Qi and D. Sun, Global and superlinear convergence of the smoothing
Newton method and its application to general box constrained variational inequalities,
Mathematics of Computation, vol. 67, pp. 519{540, 1998.
[11] R.W. Cottle, J.-S. Pang and R.-E. Stone, The Linear Complementarity Prob-
lem, Academic Press, New York, 1992.
[12] S. Dirkse, Robusr solution of mixed complementarity problems, Ph.D. Thesis, Com-
puter Sciences Department, University of Wisconsin, 1994.
[13] S. Dirkse and M. Ferris, MCPLIB: a collection of nonlinear mixed complemen-
tarity problems, Optimization Methods and Softwares, vol. 5, pp. 319{345, 1995.
[14] F. Facchinei, and J-S. Pang, Finite-Dimensional Variational Inequalities and
Complementarity Problems, Volume I, Springer, New York, 2003.
[15] F. Facchinei, and J-S. Pang, Finite-Dimensional Variational Inequalities and
Complementarity Problems, Volume II, Springer, New York, 2003.
[16] M. Ferris, C. Kanzow, and T. Munson, Feasible descent algorithms for mixed
complementarity problems, Mathematical Programming, vol. 86, pp. 475{497, 1999.
[17] M. Ferris, and J-S. Pang, Engineering and economic applications of comple-
mentarity problems, SIAM Review, vol. 39, pp. 669{713, 1997.
[18] M. Ferris and K. Sinapiromsaran, Formulating and solving nonlinear programs
as mixed complementarity problems, Optimization, volume 481 of Lecture Notes in
Economics and Mathematical Systems, edited by V. Nguyen, J. Strodiot, and P.
Tossings, 2000.
[19] A. Fischer, A special Newton-type optimization method, Optimization, vol. 24, pp.
269{284, 1992.
[20] S. A. Gabriel and J. J. More, Smoothing of mixed complementarity probblems.
In: M.C. Ferris and J. S. Pang (eds.): Complementarity and Variational Problems:
State of the Art (SIAM, Pliladelphia, Pennsylvania, 1997)105{116.
[21] P. T. Harker and J.-S. Pang, Finite dimensional variational inequality and
nonlinear complementarity problem: a survey of theory, algorithms and applications,
Mathematical Programming, vol. 48, pp. 161{220, 1990.
[22] N. J. Higham, Estimating the matrix p-norm, Numerical Mathematics, vol. 62, pp.
539{555, 1992.
[23] C. Kanzow, Some noninterior continuation methods for linear complementarity
problems, SIAM Journal on Matrix Analysis and Applications, vol. 7, pp. 851{868,
1996.
[24] C. Kanzow and S. Petra, On a semismooth least squares formulation of mixed
complementarity problems with gap reduction, Optimization Methods and Softwares,
vol. 19, pp. 507{525, 2004.
[25] C. Kanzow and S. Petra, Projected lter trust region methods for a semismooth
least squares formulation of mixed complementarity problems, Optimization Methods
and Softwares, vol. 22, pp. 713{735, 2007.