A Barzilai–Borwein type method for stochastic linear complementarity problems

Numerical Algorithms

Volumn 67, Issue 3, 2014, Pages 477-489

  Huang, Yakui ^a   Liu, Hongwei ^a   Zhou, Sha ^b  

^a XIDIAN UNIVERSITY   (China)

^b GUILIN UNIVERSITY OF ELECTRONIC TECHNOLOGY   (China)

Author keywords

Barzilai Borwein type method; Stochastic linear complementarity problem

Indexed keywords

EID: 84911001374     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-013-9803-y     Document Type: Article

References (17)

1. Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 8, 141–148 (1988)
2. Chen, C., Mangasarian, O.L.: A class of smoothing functions for nonlinear and mixed complementarity problems. Comp. Optim. Appl. 5, 97–138 (1996)
3. Chen, X.J., Fukushima, M.: Expected residual minimization method for stochastic linear complementarity problems. Math. Oper. Res. 30, 1022–1038 (2005)
4. Chen, X.J., Zhang, C.: Smoothing projected gradient method and its application to stochastic linear complementarity problems. SIAM J. Optim. 20, 627–649 (2009)
5. Chen, X.J., Zhang, C., Fukushima, M.: Robust solution of monotone stochastic linear complementarity problems. Math. Program. 117, 51–80 (2009)
6. 0 matrix linear complementarity problems. SIAM J. Optim. 18, 482–506 (2007)
7. Fischer, A.: A special Newton-type optimization method. Optimization 24, 269–284 (1992)
8. Gürkan, G., Özge, A.Y., Robinson, S.M.: Sample-path solution of stochastic variational inequalities. Math. Program. 84, 313–333 (1999)
9. Li, X.L., Liu, H.W., Sun, X.J.: Feasible smooth method based on BarzilaiCBorwein method for stochastic linear complementarity problem. Numer. Algor. 57, 207–215 (2011)
10. 1 property of an expected residual function arising from stochastic complementarity problems. Oper. Res. Lett. 36, 456–460 (2008)
11. Liu, H.W., Huang, Y.K., Li, X.L.: Partial projected Newton method for a class of stochastic linear complementarity problems. Numer. Algor. 58, 593–618 (2011)
12. Liu, H.W., Huang, Y.K., Li, X.L.: New reformulation and feasible semismooth Newton method for a class of stochastic linear complementarity problems. Appl. Math. Comput. 217, 9723–9740 (2011)
13. Liu, H.W., Li, X.L., Huang, Y.K.: Solving equations via the trust region and its application to a class of stochastic linear complementarity problems. J. Comput. Math. Appl. 61, 1646–1664 (2011)
14. Tang, J., Ma, C.F.: A smoothing Newton method for solving a class of stochastic linear complementarity problems. Nonlinear Anal. RWA 6, 3585–3601 (2011)
15. Xie, Y.J., Ma, C.F.: A smoothing Levenberg-Marquardt algorithm for solving a class of stochastic linear complementarity problem. Appl. Math. Comput. 217, 4459–4472 (2011)
16. Zhang, H., Hager, W.W.: A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14, 1043–1056 (2004)
17. Zhou, G.L., Caccetta, L.: Feasible semismooth Newton method for a class of stochastic linear complementarity problems. J. Optim. Theory Appl. 139, 379–392 (2008)