Advertisement

An inexact lagrange-newton method for stochastic quadratic programs with recourse

  • Zhou Changyin
  • He Guoping
Article
  • 31 Downloads

Abstract

In this paper, two-stage stochastic quadratic programming problems with equality constraints are considered. By Monte Carlo simulation-based approximations of the objective function and its first (second) derivative, an inexact Lagrange-Newton type method is proposed. It is showed that this method is globally convergent with probability one. In particular, the convergence is local superlinear under an integral approximation error bound condition. Moreover, this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.

MR Subject Classification

90C15 90C30 82B80 

Keywords

Lagrange-Newton method stochastic quadratic programming Monte Carlo simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Birge, J. R., Louveaux, F., Introduction to Stochastic Programming, New York: Springer-Verlag, 1997.zbMATHGoogle Scholar
  2. 2.
    Kall, P., Wallace, S. W., Stochastic Programming, Chichester: John Wiley & Sons Ltd., 1994.zbMATHGoogle Scholar
  3. 3.
    Ruszczynski, A., Decomposition methods in stochastic programming, Mathematical Programming, 1997,79:333–353.CrossRefGoogle Scholar
  4. 4.
    Rosa, C. H., Ruszczynski, A., On augmented Lagrangian decomposition methods for multistage stochastic programs, Annals of Operations Research, 1996,64:289–309.zbMATHCrossRefGoogle Scholar
  5. 5.
    Bahn, O., du Merle, O., Goffin, J. L., et al., A cutting plane method from analytic centers for stochastic programming, SIAM Journal on Optimization, 1994,4:735–753.CrossRefGoogle Scholar
  6. 6.
    Chen Xiaojun, Womersley, R. S., A parallel inexact Newton method for stochastic programs with recourse, Annals of Operation Research, 1996,64:113–141.zbMATHCrossRefGoogle Scholar
  7. 7.
    Rockafellar, R. T., Wets, R. J-B., A dual solution procedure for quadratic stochastic programs with simple recourse, in: A. Reinoza, ed., Numerical Methods, Lecture Notes in Mathematics, 1005, Berlin: Springer, 1983, 252–265.Google Scholar
  8. 8.
    Rockafellar, R. T., Wets, R. J-B., A Lagrangian finite-generation technique for solving linear-quadratic problems in stochastic programming, Mathematics Programming Study, 1986,28:63–93.zbMATHGoogle Scholar
  9. 9.
    Rockafellar, R. T., Wets, R. J-B., Linear-quadratic problems with stochastic optimization, Lecture Notes in Control and Information science, 81, Berlin: Springer, 1987, 545–560.Google Scholar
  10. 10.
    Qi Liqun, Womersley, R. S., An SQP algorithm for extended linear-quadratic problems in stochastic programming, Annals of Operations Research, 1995,56:251–285.zbMATHCrossRefGoogle Scholar
  11. 11.
    Chen Xiaojun, Qi Liqun, Womersley, R. S., Newton’s method for quadratic stochastic programs with recourse, Journal of Computational and Applied Mathematics, 1995,60:29–46.zbMATHCrossRefGoogle Scholar
  12. 12.
    Birge, J. R., Chen Xiaojun, Qi Liqun, A stochastic Newton method for stochastic quadratic programs with recourse, Applied Mathematics Report, 94/9, School of Mathematics, Univ. of New South Wales, Sydney, 1994.Google Scholar
  13. 13.
    Niederreiter, H., Random number generation and quasi-monte Carlo methods, Society for Industrial and Applied Mathematics, Philadelphia, 1992.zbMATHGoogle Scholar
  14. 14.
    Spanier, J., Maize, E. H., Quasi-random methods for estimating integrals using relatively small samples, SIAM Journal on Optimization, 1993,3:751–783.CrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities 1993

Authors and Affiliations

  • Zhou Changyin
    • 1
    • 2
  • He Guoping
    • 1
    • 2
  1. 1.Dept. of Math.Shanghai Jiaotong Univ.ShanghaiChina
  2. 2.College of Information Science and EngineeringShandong University of Science and TechnologyTaianChina

Personalised recommendations