Newton-type methods for stochastic programming

Mathematical and Computer Modelling

Volumn 31, Issue 10-12, 2000, Pages 89-98

  Chen, X ^a  

^a SHIMANE UNIVERSITY   (Japan)

Author keywords

Newton type methods; Smooth approximation techniques; Stochastic programming; Two stage stochastic linear programs with recourse

Indexed keywords

EID: 0034701972     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(00)00075-3     Document Type: Article

References (31)

1. P. Kail and S.W. Wallace, Stochastic Programming, John Wiley & Sons, (1994).
2. E.M.L. Beals, On minimizing a convex function subject to linear inequalities, J. Roy. Stat. Soc. B17, 173-184 (1955).
3. G.B. Dantzig, Linear programming under uncertainty, Management Sci. 1, 197-206 (1955).
4. X. Chen, A parallel BFGS-SQP method for stochastic linear programs, In Computational Techniques and Applications, (Edited by R.L. May and A.K. Easton), pp. 67-74, World Scientific, (1995).
5. R.T. Rockafellar and R.J.-B. Wets, A lagrangian finite-generation technique for solving linear-quadratic problems in stochastic programming, Math. Prog. Study 28, 63-93 (1986).
6. R.T. Rockafellar and R.J.-B. Wets, Linear-quadratic problems with stochastic penalties: The finite generation algorithm, In Stochastic Optimization, Lecture Notes in Control and Information Sciences 81, (Edited by V.I. Arkin, A. Shiraev and R.J.-B. Wets), pp. 545-560, Springer-Verlag, Berlin, (1987).
7. X. Chen, L. Qi and R.S. Womersley, Newton's method for quadratic stochastic programs with recourse, J. Comp. Appl. Math. 60, 29-46 (1995).
8. X. Chen and R.S. Womersley, A parallel inexact Newton method for stochastic programs with recourse, Annals Oper. Res. 64, 113-141 (1996).
9. L. Qi and R.S. Womersley, An SQP algorithm for extended linear quadratic problems in stochastic programming, Annals. Oper. Res. 56, 251-285 (1995).
10. J. Sun, K.-E. Wee and J.-S. Zhu, An interior point method for solving a class of linear-quadratic stochastic programming problems, In Recent Advances in Nonsmooth Optimization, (Edited by D.-Z. Du, L. Qi and R.S. Womersley), pp. 392-404, World Scientific, (1995).
11. C. Zhu and R.T. Rockafellar, Primal-dual projected gradient algorithms for extended linear-quadratic programming, SIAM J. Optim. 3, 751-783 (1993).
12. J.R. Birge, S.M Pollock and L. Qi, A quadratic recourse function for the two-stages stochastic program, In Progress II in Optimization: Contributions from Australasia, (Edited by X.Q. Yang. A.I. Mees, M.E. Fisher and L.S. Jennings), Kluwer Academic, Nowell, MA (to appear).
13. nd Edition, John Wiley & Sons, (1987).
14. 1 convex constrained optimization, SIAM J. Control Optim. 34, 2051-2063 (1996).
15. 1 functions and the Maratos effect, Oper. Res. Lett. 17, 131-137 (1995).
16. 1 minimization problems, J. Optim. Theory Appl. 85, 633-648 (1995).
17. 1 optimization problems, Math. Programming 64, 277-294 (1994).
18. X. Chen and R.S. Womersley, Random test problems and parallel methods for quadratic programs and quadratic stochastic programs, Optim. Methods Software (to appear).
19. E.R. Jessup, D. Yang and S.A. Zenios, Parallel factorization of structured matrices arising in stochastic programming, SIAM J. Optim. 4, 833-846 (1994).
20. A. Ruszczyński, Parallel decomposition of multistage stochastic programming problems, Math. Programming 58, 201-228 (1993).
21. J.R. Birge and F.V. Louveaux, Introduction to Stochastic Programming, Lecture Note, Department of Industrial and Operations Engineering, The University of Michigan, (1995).
22. C.-H. Tseng, Two-stage Stochastic Programming with Recourse, Master of Mathematics Thesis, University of New South Wales, (1996).
23. J.R. Birge, Decomposition and partitioning methods for multistage stochastic linear programs, Oper. Res. 33, 989-1007 (1985).
24. J.M. Mulvey, Financial planning via multi-stage stochastic optimization, Statistics and Operations Research Technical Report SOR, Princeton University 94-09 (1994).
25. R.S. Womersley and K. Lau, Portfolio optimization problems, In Computational Techniques and Applications, (Edited by R.L. May and A.K. Easton), pp. 795-802, World Scientific, (1995).
26. J.R. Birge, X. Chen and L. Qi, A stochastic method for stochastic quadratic programs with recourse, AMR, School of Mathematics, UNSW, Sydney 94/9 (1994).
27. J.L. Higle and S. Sen, Stochastic decomposition: An algorithm for two-stage linear programs with recourse, Math. Oper. Res. 16, 650-669 (1991).
28. J.R. Birge and R.J.-B. Wets, Designing approximation schemes for stochastic optimization problems, in particular, for stochastic programs with recourse, Math. Prog. Study 27, 54-102 (1986).
29. J.M. Mulvey and H. Vladinirou, Stochastic network programming for financial planning problems, Management Sci. 38, 1642-1664 (1992).
30. L. Nazareth and R.J.-B. Wets, Nonlinear programming techniques applied to stochastic programs with recourse, In Numerical Techniques in Stochastic Programming, (Edited by Y. Ermoliev and R.J.-B. Wets), pp. 95-119, Springer-Verlag, Berlin, (1988).
31. S.M. Robinson and R.J.-B. Wets, Stability in two-stage stochastic programming, SIAM J. Control. Optim. 25, 1409-1416 (1987).