A smoothing Newton method for solving a class of stochastic linear complementarity problems

Nonlinear Analysis: Real World Applications

Volumn 12, Issue 6, 2011, Pages 3585-3601

  Tang, Jia ^a   Ma, Changfeng ^a  

^a FUJIAN NORMAL UNIVERSITY   (China)

Author keywords

Convergence analysis; Numerical results; Smoothing Newton algorithm; Stochastic linear complementarity problems

Indexed keywords

CONVERGENCE ANALYSIS; GLOBAL CONVERGENCE; NEWTON ALGORITHM; NUMERICAL RESULTS; QUADRATIC CONVERGENCE; SMOOTHING NEWTON METHODS; STOCHASTIC LINEAR COMPLEMENTARITY PROBLEM;

ALGORITHMS; NEWTON-RAPHSON METHOD; STOCHASTIC SYSTEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 80052029114     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.06.017     Document Type: Article

References (26)

1. X. Chen, and M. Fukushima Expected residual minimization method for stochastic linear complementarity problems Mathematics of Operations Research 30 2005 1022 1038 (Pubitemid 43134189)
2. 1 property of an expected residual function arising from stochastic complementarity problems Operations Research Letters 36 2008 456 460
3. Steven A. Gabriel, Jifang Zhuang, and Ruud Egging Solving stochastic complementarity problems in energy market modeling using scenario reduction European Journal of Operational Research 197 2009 1028 1040
4. M. Wang, and M.M. Ali Stochastic nonlinear complementarity problems: stochastic programming reformulation and penalty based approximation method Journal of Optimization Theory and Applications 144 2010 597 614
5. M.J. Luo, and G.H. Lin Convergence results of the ERM method for nonlinear stochastic variational inequality problems Journal of Optimization Theory and Applications 142 2009 569 581
6. M.J. Luo, and G.H. Lin Expected residual minimization method for stochastic variational inequality problems Journal of Optimization Theory and Applications 140 2009 103 116
7. Xiaojun Chen, Chao Zhang, and Masao Fukushima Robust solution of monotone stochastic linear complementarity problems Mathematical Programming Series B 117 2009 51 80
8. C. Zhang, and X. Chen Stochastic nonlinear complementarity problem and applications to traffic equilibrium under uncertainty Journal of Optimization Theory and Applications 137 2008 277 295
9. R0 matrix linear complementarity problem SIAM Journal on Optimization 18 2007 482 506
10. P.T. Harker, and J.S. Pang Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications Mathematical Programming 48 1990 161 220
11. F. Facchinei, and J.-S. Pang Finite-Dimensional Variational Inequalities and Complementarity Problems, I and II 2003 Springer-Verlag New York
12. M.C. Ferris, and J.-S. Pang Engineering and economic applications of complementarity problems SIAM Review 39 1997 669 713 (Pubitemid 127661265)
13. R.W. Cottle, J.-S. Pang, and R.E. Stone The Linear Complementarity Problem 1992 Academic Press New York
14. G. Grkan, A. Y zge, and S.M. Robinson Sample-path solution of stochastic variational inequalities Mathematical Programming 84 1999 313 333
15. G.L. Zhou, and L. Caccetta Feasible semismooth Newton method for a class of stochastic linear complementarity problems Journal of Optimization Theory and Applications 139 2008 379 392
16. D.-F. Sun, R.S. Womersly, and H.-D. Qi A feaible semismooth asymptically Newton method for mixed complementarity probloms Mathematical Programming 94 2002 167 187
17. B. Chen, and N. Xiu A global linear and local quadratic non-interior continuation method for nonlinear complementarity problems based on ChenMangasarian smoothing functions SIAM Journal on Optimization 9 1999 605 623 (Pubitemid 129489297)
18. X. Chen, L. Qi, and D. Sun Global and superlinear convergence of the smoothing Newton method and its application to general box-constrained variational inequalities Mathematics of Computation 67 1998 519 540
19. B. Chen, and P.T. Harker Smoothing approximations to nonlinear complementarity problems SIAM Journal on Optimization 7 1997 403 420
20. P0-functions SIAM Journal on Optimization 10 2000 315 330
21. L. Qi, and D. Sun Improving the convergence of non-interior point algorithm for nonlinear complementarity problems Mathematics of Computation 69 2000 283 304
22. P0-NCP Acta Mathematica Sinica 26 2005 117 128 (Pubitemid 40251169)
23. C. Kanzow Global convergence properities of some interative methods for linear complementarity problems SIAM Journal on Optimization 6 1996 326 341
24. L. Qi, and J. Sun A nonsmooth version of Newton's method Mathematical Programming 58 1993 353 367
25. L. Qi Convegence analysis of some algorithms for solving nonsmooth equations Mathematics of Operations Research 18 1993 227 244
26. J.S. Pang, and L. Qi Nonsmooth equations: motivation and algorithms SIAM Journal on Optimization 3 1993 443 465