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http://dx.doi.org/10.14317/jami.2011.29.3_4.653

A HYBRID METHOD FOR NCP WITH $P_0$ FUNCTIONS  

Zhou, Qian (Department of Applied Mathematics, Hainan University)
Ou, Yi-Gui (Department of Applied Mathematics, Hainan University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 653-668 More about this Journal
Abstract
This paper presents a new hybrid method for solving nonlinear complementarity problems with $P_0$-functions. It can be regarded as a combination of smoothing trust region method with ODE-based method and line search technique. A feature of the proposed method is that at each iteration, a linear system is only solved once to obtain a trial step, thus avoiding solving a trust region subproblem. Another is that when a trial step is not accepted, the method does not resolve the linear system but generates an iterative point whose step-length is defined by a line search. Under some conditions, the method is proven to be globally and superlinearly convergent. Preliminary numerical results indicate that the proposed method is promising.
Keywords
nonlinear complementarity problem; ODE-based method; smoothing trust region method; global convergence; superlinear convergence;
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1 J.S.Chen, C.H.Ko and S.H.Pan, A neural network based on the generalized Fischer- Burmeister function for nonlinear complementarity problems, Information Sciences 180 (2010), 697-711.   DOI   ScienceOn
2 J.L.Zhang and X.S.Zhang, A smoothing Levenberg-Marquardt method for NCP, Applied Mathematics and Computation 178 (2006), 212-228.   DOI   ScienceOn
3 L.Q.Qi, Convergence analysis of some algorithms for solving nonsmooth equations, Mathematics of Operations Research 18(1993), 227-244.   DOI   ScienceOn
4 C.Kanzow, Some non-interior continuation methods for linear complementarity problems, SIAM Journal on Matrix Analysis and Application 17(1996), 851-868.   DOI   ScienceOn
5 Y.F.Yang and L.Q.Qi, Smoothing trust region methods for nonlinear complementarity prob- lems with P0-functions, Annals of Operations Research, 133(2005), 99-117.   DOI
6 F.H.Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, 1983.
7 Kanzow C and Pieper H, Jacobian smoothing methods for nonlinear complementarity problem, SIAM Journal on Optimization 9(1999), 342-373.   DOI   ScienceOn
8 E.M.Gertz, A quasi-Newton trust region method, Mathematical Programming(Series A) 100 (2004), 447-470.
9 S.J.Qu, M.Goh and X.J.Zhang, A new hybrid method for nonlinear complementarity problems, Computational Optimization and Applications, Doi 10.1007/s10589-009-9309-7.
10 A.A.Brown and M.C.Biggs, Some effective methods for unconstrained optimization based on the solution of system of ordinary differentiable equations, Journal of Optimization Theory and Application 62(1989), 211-224.   DOI   ScienceOn
11 Y.Zhou, A smoothing conic trust region filter method for the nonlinear complementarity problem, Journal of Computational and Applied Mathematics, 229(2009), 248-263.   DOI   ScienceOn
12 Y.X,Yuan,W.Y.Sun, Optimization Theory and Methods, Science Press, Beijing, 1997.
13 J.Y.Han, N.H.Xiu and H.D.Qi, Nonlinear Complementarity: Theory and Algorithm, Shang- hai Science and Technology Press, Shanghai, 2006.
14 X.J.Chen, Smoothing methods for complementarity problems and their applications: A Survey, Journal of the Operations Research Society of Japan, 43(1)(2000), 32-47.   DOI
15 Z.S.Yu, K.Su and J.Lin, A smoothing Levenberg-Marquardt method for the extended linear complementarity problem, Applied Mathematical Modelling, 33(8)(2009), 3409-3420.   DOI   ScienceOn
16 J.Long, C.F.Ma and P.Y.Ni, A new filter method for solving nonlinear complementarity problems, Applied Mathematics and Computation, 185(2007), 705-718.   DOI   ScienceOn
17 J.Nocedal and Y.X.Yuan, Combing trust region and line search techniques, In: Y.X.Yuan, ed, Advances in Nonlinear programming, Kluwer, 1998, 153-175.
18 S.P.Rui and C.X.Xu, A smoothing inexact Newton method for nonlinear complementarity problems, Journal of Computational and Applied Mathematics, 233(2010), 2332-2338.   DOI   ScienceOn