A smoothing Levenberg-Marquardt method for the extended linear complementarity problem

Applied Mathematical Modelling

Volumn 33, Issue 8, 2009, Pages 3409-3420

  Yu, Zhensheng ^a   Su, Ke ^b   Lin, Ji ^a  

^a UNIVERSITY OF SHANGHAI FOR SCIENCE AND TECHNOLOGY   (China)

^b HEBEI UNIVERSITY   (China)

Author keywords

Extended linear complementarity; Global convergence; Levenberg Marquardt method; Local superlinear convergence; Smoothing function

Indexed keywords

EXTENDED LINEAR COMPLEMENTARITY; GLOBAL CONVERGENCE; LEVENBERG-MARQUARDT METHOD; LOCAL SUPERLINEAR CONVERGENCE; SMOOTHING FUNCTION;

SUPPORT VECTOR MACHINES;

EID: 64249100922     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2008.11.004     Document Type: Article

References (31)

1. Mangasarian O.L., and Pang J.S. The extended linear complementarity problem. SIAM J. Matrix Anal. Appl. 16 (1995) 359-368
2. Gowda M.S. On reducing a monotone horizontal LCP to an LCP. Appl. Math. Lett. 8 (1995) 97-100
3. Gowda M.S. On the extended linear complementarity problems. Math. Program. 72 (1996) 33-50
4. Andreani R., and Martinez J.M. On the resolution of the extended linear complementarity problem. Linear Algebra Appl. 281 (1997) 247-257
5. Solodov M.V. Some optimization reformulations of the extended linear complementarity problem. Comput. Optim. Appl. 13 (1999) 187-200
6. Chen B., and Harker P.T. A noninterior point continuation method for linear complementarity problems. SIAM J. Matrix Anal. Appl. 14 (1994) 168-1190
7. Chen X. Smoothing methods for complementarity problems and their applications: a survey. J. Oper. Res. Soc. Jpn. 43 (2000) 2-47
8. Chen X., Qi L., and Sun D. Global and superlinear convergence of the smoothing Newton method and its applications to general box constrained variational inequalities. Math. Comput. 222 (1999) 519-540
9. Qi L., Sun D., and Zhou G. A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities. Math. Program. 87 (2000) 1-35
10. Engelke S., and Kanzow C. On the solution of linear programming by Jacobian smoothing methods. Ann. Oper. Res. 103 (2002) 49-70
11. 0 functions. Ann. Oper. Res. 133 (2005) 99-117
12. Xiu N.H., and Zhang J.Z. A smoothing Guass-Newton method for the generalized HLCP. J. Comput. Appl. Math. 129 (2001) 195-208
13. S.C. Fang, J.Y. Han, Z.H. Huang, S.I. Birbil, On the Finite Termination of an Entropy Function based Smoothing Newton Method for Vertical Linear Complementarity Problems, CoA, 2003.
14. Fischer A. A special Newton-type Optimization methods. Optimization 24 (1992) 269-284
15. Kanzow C. Some noninterior continuation method for linear complementarity problems. SIAM J. Matrix Anal. Appl. 17 (1996) 851-868
16. Chen B., Chen X., and Kanzow C. A penalized Fischer-Burmeister NCP-function. Math. Program. 88 (2000) 211-216
17. Fan J.Y. A modified Levenberg-Marquardt algorithm for singular system of nonlinear equations. J. Comput. Math. 21 (2003) 625-636
18. Kanzow C., and Zupke M. Inexact trust region methods for nonlinear complementarity problems. In: Fukushima M., and Qi L. (Eds). Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods (1998), Kulwer Academic Press, Norwell, MA 211-233
19. Kanzow C., Nagel C., and Fukushima M. Successive linearization methods for nonlinear semidefinite programmings. Comput. Optim. Appl. 19 (2005) 251-273
20. Powell M.J.D. Convergence properties of a class of minimization algorithms. In: Mangasarian O.L., Meyer R.R., and Robinson S.M. (Eds). Nonlinear Programming 2 vol. 21 (1984), Acdemic Press 815-843
21. 0 (P)-properties; extended vertical and horizontal LCPs. Linear Algebra Appl. 94 (1997) 449-467
22. Dennis J.E., and Schnabel R.B. Numerical Methods for unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall, Englewood Cliffs, NJ
23. Facchinei F., and Soares J. A new merit function for nonlinear complementarity problems and a related algorithm. SIAM J. Optim. 7 (1997) 225-247
24. Qi L. Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18 (1993) 227-244
25. Kanzow C. On a semismooth least squares formulation of complementarity problem with gap reduction. Optim. Meth. Software 19 (2004) 507-525
26. Harker P.T., and Pang J.-S. A damped Newton method for the linear complementarity problem. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics vol. 26 (1990), AMS, Providence, Rhode Island 265-284
27. Friedlander A., Martínez J.M., and Santos S.A. Solution of linear complementarity problems using minimization with simple bounds. J. Global Optim. 6 (1995) 253-267
28. Murty K.G. Linear complementarity, linear and nonlinear programming. Sigma Series in Applied Mathematics 3 (1988), Heldermann Verlag, Berlin, Germany
29. Clarke F.H. Optimization and Nonsmooth Analysis. second ed. Classic Appl. Math. vol. 5 (1990), SIAM, Philadephia, PA
30. Cottle R.W., Pang J.S., and Stone R.E. The Linear Complementarity Problem (1992), Academic Press, New York
31. Kanzow C., and Petra S. An inexact semismooth least square method for large scale complementarity problem. Optim. Meth. Software 19 (2004) 309-325