Email this article A Mixed Algorithm for Nonlinear Complementarity Problems
Abstract
Combining nonmonotone trust region algorithms and PSO methods, we propose a mixed method for nonlinear complementarity problems. The iterative formula of μk is very simple. When the determinant of Bk +λkI is very large or small, the PSO method will obtain a new point which gets us better astringency. Numerical test results show the effectiveness of this algorithm.
Keywords
References
[1] M. C. Ferris, M. C. Ferris, J. S. Pang, "Engineering and economic applications of complementarity problems," J. SIAM Eview. Vol. 39, pp. 669-713, 1997.
http://dx.doi.org/10.1137/S0036144595285963
[2]J. Burke, S. Xu, "The global linear convergence of a Non-interior path-following algorithm for linear complementarity problems," J. Math Oper Res. Vol. 23, pp. 719-734,1998.
http://dx.doi.org/10.1287/moor.23.3.719
[3]K. Hotta, Yoshise, "A global convergence of a Class of Non-interior-Point algorithms Using Chen-Harker-Kanzow Functions for linear complementarity problems," J. Mathematical Programming. Vol. 86, pp. 105-133, 1999.
http://dx.doi.org/10.1007/s101070050082
[4]S. Xu, "The global linear convergence of aninfeasible non-interior path-following algorithm for complementarity problems with uniform P-functions," J. Mathematical Programming. Vol. 87, pp. 501-517, 2000.
http://dx.doi.org/10.1007/s101070050009
[5]B. Chen, P. T. Harker, "A non-interior-point continuation method for linear complementarity problems," J. SIAM. Journal of Matrix Analysis and Application. Vol. 14, pp. 1168-1190, 1993.
http://dx.doi.org/10.1137/0614081
[6]H. D. Yu, D. G. Pu, “A nonmonotone trust region algorithm of nonlinear complementarity problem,” D. Shang Hai, College of Science of tong ji university, 2008.
[7]J. Y. Han, N. H. Xiu, H. D. Qi,Theory and Algorithms for Nonlinear Complementarity. ShangHai, CA: Shanghai Science and Technology Press, 2006.
[8]Y. Yuan, "On the superlinear convergence of a trust region algorithm for nonsmooth optimization," J. Math Prog. Vol. 31, pp. 269-285, 1985.
http://dx.doi.org/10.1007/BF02591949
[9]Y. Yuan, "Conditions for convergence of trust region algorithms for nonsmooth optimization," J. Math Prog. Vol. 31, pp. 220-228, 1985.
http://dx.doi.org/10.1007/BF02591750
[10]J. X. Dong, X. Y. Wang, "A smoothing self-trust region method for the NCP(F)," J. Journal of Southwest University for Nationalities. Vol. 35, pp. 973-977, 2009.
[11]W. M. Chen, Y. F. Yang, "Smoothing methods for solving general nonlinear complementarity problems," J. Or Transactions. Vol. 12, pp. 93-103, 2008.
[12]C. F. Ma. "The smooth trust region algorithm for nonlinear complementarity problems," J. Chinese Journal of Engineering Mathematics. Vol. 23, pp. 20-28, 2006.
[13]Y. F. Yang,"Smoothing trust region methods for nonlinear complementarity problems with P0-functions," J. Annals of Operations Research. Vol. 133, pp. 99-177, 2005.
http://dx.doi.org/10.1007/s10479-004-5026-x
[14]N. I. M. Gould, S. Lucidi, M. Roma, P. L. Toint, "A line search algorithm with memory for unconstrained optimization," J. Kluwer Academic Publishers. Vol. 3, pp. 207-223, 1998.
[15]H. M. Cui, Q. B. Zhu, "Convergence analysis and parameter selection in particle swarm optimization," J. Computer Engineering and Applications. Vol. 23, pp. 89-91, 2007.
[16]Y. Wang, X. Y. Wang, "Completely mooth trust region algorithm for nonlinear complementarity problem," J. Journal of Southwest University for Nationalities. in press.
[17]Y. G. Ou, "Trust region algorithm for a class of nonlinear complementarity problem," J. Math. China, Vol. 22, pp. 558-566, 2004.
[18]Y. L. Zhao, “A new nonmonotonic trust region method,” J. Journal of Xi Dian University. Vol. 24, pp .486-491,1997 .
Full Text: PDF