|
|
|
A smoothing inexact Newton method for P0 nonlinear complementarity problem |
Haitao CHE1,2( ), Yiju WANG2, Meixia LI1 |
| 1. School of Mathematics and Information Science, Weifang University,Weifang 261061, China; 2. School of Management Science, Qufu Normal University, Rizhao 276800, China |
|
|
|
|
Abstract We first propose a new class of smoothing functions for the nonlinear complementarity function which contains the well-known Chen-Harker- Kanzow-Smale smoothing function and Huang-Han-Chen smoothing function as special cases, and then present a smoothing inexact Newton algorithm for the P0 nonlinear complementarity problem. The global convergence and local superlinear convergence are established. Preliminary numerical results indicate the feasibility and efficiency of the algorithm.
|
| Keywords
Nonlinear complementarity problem (NCP)
inexact Newton methods
P0-function
smoothing function
|
|
Corresponding Author(s):
CHE Haitao,Email:haitaoche@163.com
|
|
Issue Date: 01 December 2012
|
|
| 1 |
Chen B, Harker P T. A non-interior-point continuation method for linear complementarity problems. SIAM J Matrix Anal Appl , 1993, 14(4): 1168-1190 doi: 10.1137/0614081
|
| 2 |
Chen B, Ma C. A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P0 function. J Global Optim , 2011, 51(3): 473-495 doi: 10.1007/s10898-010-9640-7
|
| 3 |
Chen X, Qi L, Sun D. Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities. Math Comput , 1998, 67(222): 519-540 doi: 10.1090/S0025-5718-98-00932-6
|
| 4 |
Clarke F H. Optimization and Nonsmooth Analysis. New York: Wiley, 1983
|
| 5 |
Ferris M C, Pang J S. Engineering and economic applications of complementarity problems. SIAM Review , 1997, 39(4): 669-713 doi: 10.1137/S0036144595285963
|
| 6 |
Geiger C, Kanzow C. On the resolution of monotone complementarity problems. Comput Optim Appl , 1996, 5: 155-173 doi: 10.1007/BF00249054
|
| 7 |
Harker P T, Pang J S. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Math Program , 1990, 48(2): 161-220 doi: 10.1007/BF01582255
|
| 8 |
Hotta K, Yoshise A. Global convergence of a class of non-interior point algorithms using Chen-Harker-Kanzow-Smale functions for nonlinear complementarity problems. Math Program , 1999, 86: 105-133 doi: 10.1007/s101070050082
|
| 9 |
Huang Z, Han J, Chen Z. Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P0 Function. J Optim Theory Appl , 2003, 117(1): 39-68 doi: 10.1023/A:1023648305969
|
| 10 |
Kanzow C. Some noninterior continuation methods for linear complementarity problems. SIAM J Matrix Anal Appl , 1996, 17(4): 851-868 doi: 10.1137/S0895479894273134
|
| 11 |
Kanzow C, Kleinmichel H. A new class of semismooth Newton-type methods for nonlinear complementarity problems. Comput Optim Appl , 1998, 11: 227-251 doi: 10.1023/A:1026424918464
|
| 12 |
Luca T D, Facchinei F, Kanzow C. A semismooth equation approach to the solution of nonlinear complementarity problems. Math Program , 1996, 75(3): 407-439 doi: 10.1007/BF02592192
|
| 13 |
Ma C, Chen X. The convergence of a one-step smoothing Newton method for P0-NCP base on a new smoothing NCP-function. J Comput Appl Math , 2008, 216(1): 1-13 doi: 10.1016/j.cam.2007.03.031
|
| 14 |
Mathiesen L. An algorithm based on a sequence of a linear complementarity problems applied to a Walrasian equilibrium model: an example. Math Program , 1987, 37(1): 1-18 doi: 10.1007/BF02591680
|
| 15 |
Mifflin R. Semismooth and semiconvex functions in constrained optimization. SIAM J Control Optim , 1977, 15(6): 957-972 doi: 10.1137/0315061
|
| 16 |
Natasa K, Sanja R. Globally convergent Jacobian smoothing inexact Newton methods for NCP. Comput Optim Appl , 2008, 41(2): 243-261 doi: 10.1007/s10589-007-9104-2
|
| 17 |
Pang J S, Gabriel A. NE/SQP: a robust algorithm for nonlinear complementarity problems. Math Program , 1993, 60: 295-337 doi: 10.1007/BF01580617
|
| 18 |
Qi L. Convergence analysis of some algorithms for solving nonsmooth equations. Math Oper Res , 1993, 18(1): 227-244 doi: 10.1287/moor.18.1.227
|
| 19 |
Qi L, Sun D, Zhou G. A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities. Math Program , 2000, 87(1): 1-35
|
| 20 |
Qi L, Sun J. A nonsmooth version of Newton’s method. Math Programming , 1993, 58(3): 353-367 doi: 10.1007/BF01581275
|
| 21 |
Sun D, Qi L. On NCP functions. Comput Optim Appl , 1999, 13: 201-220 doi: 10.1023/A:1008669226453
|
| 22 |
Xie D, Ni Q. An incomplete Hessian Newton minimization method and its application in a chemical database problem. Comput Optim Appl , 2009, 44(3): 467-485 doi: 10.1007/s10589-008-9164-y
|
| 23 |
Zhang X, Jiang H, Wang Y. A smoothing Newton method for generalized nonlinear complementarity problem over a polyhedral cone. J Comput Appl Math , 2008, 212: 75-85 doi: 10.1016/j.cam.2006.03.042
|
| 24 |
Zhang J, Zhang K. A variant smoothing Newton method for P0-NCP based on a new smoothing function. J Comput Appl Math , 2009, 225(1): 1-8 doi: 10.1016/j.cam.2008.06.012
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|