Browse > Article
http://dx.doi.org/10.14317/jami.2014.211

A SMOOTHING NEWTON METHOD FOR NCP BASED ON A NEW CLASS OF SMOOTHING FUNCTIONS  

Zhu, Jianguang (School of Science, Shandong University of Science and Technology)
Hao, Binbin (School of Science, China University of Petroleum)
Publication Information
Journal of applied mathematics & informatics / v.32, no.1_2, 2014 , pp. 211-225 More about this Journal
Abstract
A new class of smoothing functions is introduced in this paper, which includes some important smoothing complementarity functions as its special cases. Based on this new smoothing function, we proposed a smoothing Newton method. Our algorithm needs only to solve one linear system of equations. Without requiring the nonemptyness and boundedness of the solution set, the proposed algorithm is proved to be globally convergent. Numerical results indicate that the smoothing Newton method based on the new proposed class of smoothing functions with ${\theta}{\in}(0,1)$ seems to have better numerical performance than those based on some other important smoothing functions, which also demonstrate that our algorithm is promising.
Keywords
Nonlinear complementarity problem; Smoothing Newton method; Global linear convergence; Local superlinear convergence;
Citations & Related Records
연도 인용수 순위
  • Reference
1 F.A.Potra, Y.Ye . Interior-point methods for nonlinear complementarity problems, J. Optim. Theory Appl. 88 (3)(1996) 617-642.   DOI
2 S. Wright, D. Ralph, A superlinear infeasible-interior-point algorithm for monotone com-plementarity problems, Math. Oper. Res. 21(4)(1996) 815-838.   DOI   ScienceOn
3 K. Hotta, A. Yoshise, Global convergence of a class of non-interior point algorithms using Chen-Harker-Kanzow-Smale functions for nonlinear complementarity problems, Math. Program. 86(1)(1999) 105-133.   DOI
4 L. Qi, D. Sun, G. Zhou, A new look at smoothing Newton methods for nonlinear complemen-tarity problems and box constrained variational inequalities, Math. Program. 87(1)(2000) 1-35.   DOI
5 L. Fang, A new one-step smoothing Newton method for nonlinear complementarity problem with P0-function, Appl. Math. Comput. 216 (2010) 1087-1095.   DOI   ScienceOn
6 C.Kanzow, Some noninterior continuation methods for linear complementarity problems, SIAM J. Matrix Anal. Appl. 17(1996) 851-868.   DOI   ScienceOn
7 C.Chen, O.L.Mangasarian, A Class of Smoothing Functions for Nonlinear and Mixed Com-plementarity Problems, Comput. Optim. Appl. 5 (1996) 97-138.   DOI
8 Z.H.Huang, J.Han, Z.Chen . 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. 117(1)(2003) 39-68.   DOI   ScienceOn
9 Z.H.Huang, J.Han, D.C.Xu, L.P.Zhang, The non-interior continuation methods for solving the P0 function nonlinear complementarity problem, Science in China, 44(9) (2001) 1107-1114   DOI   ScienceOn
10 X. Liu, W.Wu, Coerciveness of some merit functions over symmetric cones, J. Ind. Manag. Optim. 5(2009)603-613.   DOI
11 M.Kojima, N.Megiddo, T.Noma, Homotopy continuation methods for nonlinear comple-mentarity problems, Math. Oper. Res. 16 (1991) 754-774.   DOI
12 B.Chen, P.T.Harker, A non-interior continuation algorithm for linear complementarity problems, SIAM J. Matrix Anal. Appl. 14 (1993) 1168-1190.   DOI   ScienceOn
13 C. Kanzow, Global convergence properties of some iterative methods for linear comple-mentarity problems, SIAM J. Optim. 6 (1) (1996), 326-341.   DOI   ScienceOn
14 Z.H. Huang, Y. Zhang, W. Wu, A smoothing-type algorithm for solving system of inequal-ities, J. Comput. Appl. Math. 220 (1) (2008) 355-363.   DOI   ScienceOn
15 J.S.Pang, S.A.Gabriel, NE/SQP: A robust algorithm for the nonlinear complementarity problem, Math. Program. 60 (1993) 295-337.   DOI
16 O.L.Mangasarian, M.V.Solodov, Nonlinear complementarity as unconstrained and con-strained minimization, Math. Program. 62 (1993) 277-297.   DOI
17 C.Kanzow, Some equation-based methods for the nonlinear complementarity problem, Optim. Meth. Soft. 3 (1994) 327-340.   DOI   ScienceOn
18 H.Jiang, L.Qi, A new nonsmooth eqations approach to nonlinear complementarity problems, SIAM J. Control Optim. 35 (1997) 178-193.   DOI   ScienceOn
19 W.Hock, K.Schittkowski, Test examples for nonlinear programming codes, Lecture Notes in Economics and Mathematical Systems 187, Springer-Verlag: Berlin, Germany, (1981).
20 S.P.Dirkse, M.C.Ferris, MCPLIB: A collection of nonlinear mixed complementarity problems, Optim. Meth. Soft. 5 (1995) 319-345.   DOI
21 M.C.Ferris, J.S.Pang, Engineering and economic applications of complementarity problems, SIAM Review 39 (1997) 669-713.   DOI   ScienceOn
22 P.T.Harker,J.-S.Pang, Finite dimensional variational inequality and nonlinear complemen-tarity problem: A survey of theory, algorithms and applications, Math. Program. 48 (1990) 161-220.   DOI   ScienceOn