Frontiers of Mathematics in China >
A smoothing inexact Newton method for P0 nonlinear complementarity problem
Received date: 12 May 2011
Accepted date: 10 Sep 2012
Published date: 01 Dec 2012
Copyright
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.
Haitao CHE , Yiju WANG , Meixia LI . A smoothing inexact Newton method for P0 nonlinear complementarity problem[J]. Frontiers of Mathematics in China, 2012 , 7(6) : 1043 -1058 . DOI: 10.1007/s11464-012-0245-y
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
|
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
|
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
|
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
|
6 |
Geiger C, Kanzow C. On the resolution of monotone complementarity problems. Comput Optim Appl, 1996, 5: 155-173
|
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
|
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
|
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
|
10 |
Kanzow C. Some noninterior continuation methods for linear complementarity problems. SIAM J Matrix Anal Appl, 1996, 17(4): 851-868
|
11 |
Kanzow C, Kleinmichel H. A new class of semismooth Newton-type methods for nonlinear complementarity problems. Comput Optim Appl, 1998, 11: 227-251
|
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
|
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
|
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
|
15 |
Mifflin R. Semismooth and semiconvex functions in constrained optimization. SIAM J Control Optim, 1977, 15(6): 957-972
|
16 |
Natasa K, Sanja R. Globally convergent Jacobian smoothing inexact Newton methods for NCP. Comput Optim Appl, 2008, 41(2): 243-261
|
17 |
Pang J S, Gabriel A. NE/SQP: a robust algorithm for nonlinear complementarity problems. Math Program, 1993, 60: 295-337
|
18 |
Qi L. Convergence analysis of some algorithms for solving nonsmooth equations. Math Oper Res, 1993, 18(1): 227-244
|
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
|
21 |
Sun D, Qi L. On NCP functions. Comput Optim Appl, 1999, 13: 201-220
|
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
|
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
|
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
|
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