Solving equations via the trust region and its application to a class of stochastic linear complementarity problems

Computers and Mathematics with Applications

Volumn 61, Issue 6, 2011, Pages 1646-1664

  Liu, Hongwei ^a   Li, Xiangli ^a   Huang, Yakui ^a  

^a XIDIAN UNIVERSITY   (China)

Author keywords

Equations; Semi smooth; Stochastic linear complementarity; Trust region method

Indexed keywords

BOX CONSTRAINTS; COMPLEMENTARITY PROBLEMS; EQUATIONS; EXISTING METHOD; LOCAL QUADRATIC CONVERGENCE; NUMERICAL RESULTS; QUADRATIC CONVERGENCE; SEMI-SMOOTH; STOCHASTIC LINEAR COMPLEMENTARITY; STOCHASTIC LINEAR COMPLEMENTARITY PROBLEM; TRUST REGION; TRUST REGION METHOD;

ALGORITHMS; STOCHASTIC SYSTEMS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 79952440904     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.01.033     Document Type: Article

References (25)

1. F. Facchinei, and J.J. Judice An active set Newton algorithm for large-scale nonlinear programs with box constraints SIAM Journal on Optimization 8 1998 158 186
2. C. Kanzow, and A. Klug An interior-point affine-scaling trust-region method for semismooth equations with box constraints Computational Optimization and Applications 37 2007 329 353 (Pubitemid 47139045)
3. C. Kanzow, An active-set type Newton method for constrained nonlinear systems, in: Michael C. Ferris and Olvi L. Mangasarian and Jong-Shi Pang, pp. 179200 (Chapter 9).
4. Y.-H. Dai, and R. Fletcher Projected BarzilaiBorwein methods for large-scale box-constrained quadratic programming Numerische Mathematik 100 2005 21 47 (Pubitemid 40405555)
5. S. Bellavia, M. Macconi, and B. Morini An affine scaling trust-region approach to bounded-constrained nonlinear systems Applied Numerical Mathematics 44 2003 257 280
6. H. Qi, L. Qi, D. Sun, Solving KKT systems via the trust region and the conjugate gradient methods, Technical Report, Applied Mathematics Research Report AMR99/19, School of Mathematics, University of New South, 1999.
7. L. Qi, X. Tong, and D.H. Li Active-set projected trust region algorithm for box constrained nonsmooth equations Journal of Optimization Theory and Applications 120 2004 601 625 (Pubitemid 39046636)
8. D. Sun, R.S. Womersley, and H. Qi A feasible semismooth asymptotically Newton method for mixed complementarity problems Mathematical Programming 94 2002 167 187 (Pubitemid 44744735)
9. F.H. Clarke Optimization and Nonsmooth Analysis 1983 John Wiley and Sons
10. J. Han, N. Xiu, and H. Qi Theories and Algorithms for Nonlinear Complementarity Problems 2006 ShangHai Science and Technology Press
11. J.-B. Hiriart-Urruty, J.-J. Strodiot, and V.H. Nguyen Generalized Hessian matrix and second-order optimality conditions for problems with c 1' 1 data Applied Mathematics and Optimization 11 1984 43 56 (Pubitemid 14585265)
12. J. Nocedal, and S.J. Wright Numerical Optimization 1999
13. F. Facchinei, and J.-S. Pang Finite-Dimensional Variational Inequalities and Complementarity Problems 2003
14. F. Facchinei, A. Fischer, and C. Kanzow On the accurate identification of active conatraints SIAM Journal on Optimization 9 1998 14 32
15. X. Chen, and M. Fukushima Expected residual minimization method for stochastic linear complementarity problems Mathematics of Operations Research 30 2005 1022 1038 (Pubitemid 43134189)
16. B. Chen, X. Chen, and C. Kanzow A penalized FischerBurmeister NCP-function Mathematical Programming 88 2000 211 216
17. A. Fischer Solution of monotone complementarity problems with locally Lipschitzian functions Mathematical Programming 76 1997 513 532 (Pubitemid 127380006)
18. F. Facchinei, and C. Kanzow A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems Mathematical Programming 76 1997 493 512 (Pubitemid 127380005)
19. D. Sun A regularization Newton method for solving nonlinear complementarity problems Applied Mathematics and Optimization 40 1999 315 339
20. G. Gürkan, A.Y. zge, and S.M. Robinson Sample-path solution of stochastic variational inequalities Mathematical Programming 84 1999 313 333
21. G. Zhou, and L. Caccetta Feasible semismooth Newton method for a class of stochastic linear complementarity Journal of Optimization Theory and Applications 139 2008 379 392
22. H. Fang, X. Cheng, and M. Fukushima Stochastic R 0 matrix linear complementarity problems SIAM Journal on Optimization 18 2007 482 506
23. G.-H. Lin, and M. Fukushima New reformulations for stochastic nonlinear complementarity problems Optimization Methods and Software 21 2006 551 564 (Pubitemid 43982754)
24. G.-H. Lin, X. Chen, and M. Fukushima New restricted NCP functions and their applications to stochastic NCP and stochastic MPEC Optimization 56 2007 641 653
25. X. Chen, and C. Zhang Robust solution of monotone stochastic linear complementarity problems Mathematical Programming 117 2008 51 80