Skip to main content
SpringerLink
Log in

Asynchronous nested optimization algorithms and their parallel implementation

  • Evolutionary Computation and Distributed Computation
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

Large scale optimization problems can only be solved in an efficient way, if their special structure is taken as the basis of algorithm design. In this paper we consider a very broad class of large — scale problems with special structure, namely tree structured problems. We show how the exploitation of the structure leads to efficient decomposition algorithms and how it may be implemented in a parallel environment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dempster M A H.Stochastic Programming. London: Academic Press, 1980.

    MATH  Google Scholar 

  2. Dempster M A H. On Stochastic Programming II: Dynamic Problems Under risk.Stochastics, 1988,25: 15–42.

    MATH  MathSciNet  Google Scholar 

  3. Dupacova J. Multistage Stochastic Programs: The State-of-art and Selected Bibliography.Kybernetika, 1995,31:151–174.

    MATH  MathSciNet  Google Scholar 

  4. Ermoliev Y, Wets R J B. eds.Numerical Techniques for Stochastic Optimization. Berlin: Springer-Verlag, 1988.

    MATH  Google Scholar 

  5. Kall P, Wallace S W.Stochastic Programming. John Wiley, 1994.

  6. Pereirea M V F, Pinto L M. Multe-Stage Stochastic Optimization Applied to Energy Planning.Math Programming, 1991,52:359–375.

    Article  MathSciNet  Google Scholar 

  7. Somlyody L, Wets R J B. Stochastic Optimization Models for Lake Eutrophication Management.Oper Res, 1988,36:660–681.

    Article  MATH  MathSciNet  Google Scholar 

  8. Wets R J B. Large Scale Linear Programing Techniques. In: Er-moliev Y, Wets R J B, eds.Numerical Techniques for Stochastic Optimization. Springer-Verlag, 1988. 65–94.

  9. Bradley S P, Crane D B. A Dynamic Model for Bond Porfolio Management.Management Sci, 1972,19: 139–151.

    Article  Google Scholar 

  10. Dempster M A H, Ireland A M. A Financial Expert Decision Support System. In: Mitra G, ed.Mathematical Models for Decision Support. Springer-Verlag, 1988. 631–640.

  11. Dempster M A H, Ireland A M. Object Oriented Nmodel Integration in a Financial Decision Support System.Decision Support Systems, 1991,7:1–12.

    Article  Google Scholar 

  12. Hutchinson P, Lane M. A Model for Managing a Certificate of Deposit Portfolio Under Uncertainty. In: Dempster M A H, ed.Stochastic Programming. Academic Press, 1980. 473–496.

  13. Kusy M I, Ziemba W T. A Bank Asset and Liability Model.Oper Res, 1986,34:356–376.

    Article  Google Scholar 

  14. Bienstock D, Shapiro J F. Optimizing Resource Acquisition Decisions by Stochastic Programming.Management Sci, 1988,34:215–229.

    Article  Google Scholar 

  15. Suhl U H. MOPS-Mathematical Optimization System.European J Oper Res, 1994,72:312–322.

    Article  MATH  Google Scholar 

  16. Lustig I J, Marsten R E, shanno D F. Interior Point Methods for Linear Programming: Computational State of the art.ORSA J Comput, 1994,6:1–14.

    MATH  MathSciNet  Google Scholar 

  17. Wright S J. Primal-Dual Interior-Point Methods. Society for Industrial and Applied Mathematics, Philadelphia, 1997.

    MATH  Google Scholar 

  18. Bertsekas D P.Constrained Optimization and Lagrange Multiplier Methods. New York: Academic Press, 1982.

    MATH  Google Scholar 

  19. Ruszczynski A. Decomposition Methods in Stochastic Programming.Math Programming, 1997,79: 333–353.

    MathSciNet  Google Scholar 

  20. Benders J F. Partitioning Procedures for Solving Mixed-Variable Programming Problems.Numer Math, 1962,4:238–252.

    Article  MATH  MathSciNet  Google Scholar 

  21. Gassmann H I. MSLiP: A Computer Code for the Multistage Stochastic Linear Programming Problem.Math Programming, 1990,47:407–423.

    Article  MATH  MathSciNet  Google Scholar 

  22. Kallberg J G, Ziemba W T. An Algorithm for Portfolio revision: Theory, Computational Algorithm and Empirical Results. In: Shultz R, ed.Applications of Management Science. JAI Press. 1981. 267–291.

  23. Lasdon L S. Optimization Theory for Large Systems. Macmillan Series in Operations Research, London, 1970.

  24. Levkovitz R, Mitra G. Solution of Large-Scale Linear Programs: A Review of Hardware. Software and Algorithmic Issues. In: Ciriani T A, Leachman R C, eds.Optimization in Industry. John Wiley. 1993. 139–171.

  25. Ariyawansa K A, Hudson D D. Performance of a Benchmark Parallel Implementation of the Van-Slyke and Wets Algorithm. Concurrency: Practice and Experience, 1991,3:109–128.

    Article  Google Scholar 

  26. Pflug G C, Swietanowski A. Selected Parallel Pptimization Methods for Financial Management Under Uncertainty.Parallel Comput, 2000,26:3–25.

    Article  MATH  Google Scholar 

  27. Ruszczynski A. Parallel Decompositin of Multistage Stochastic Programming Problems.Math Programming, 1993,58:201–228.

    Article  MATH  MathSciNet  Google Scholar 

  28. Lea D.Concurrent Programming in Java. Addison-Wesley, 1997.

  29. Hitz M, Kappel G. UML@Qwork. Dpunkt, 1999.

  30. Rumbough J, Jacobson I, Booch G.The Unified Modelling Language Reference Manual. Addison Wesley, 1999.

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Decision Support Systems, University of Vienna, Universitaetsstrasse 5, A-1090, Vienna, Austria

    Hans W. Moritsch, G. Ch. Pflug & M. Siomak

Authors
  1. Hans W. Moritsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ch. Pflug
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Siomak
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Foundation item: Supported by the Austrin Science Fund as part of the Special Research Program AURORA(f011)

Biography: Hans W. Moritsch (1959-), male, Research Scientist, Dipl.-Ing., research direction: parallel optimization.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moritsch, H.W., Pflug, G.C. & Siomak, M. Asynchronous nested optimization algorithms and their parallel implementation. Wuhan Univ. J. of Nat. Sci. 6, 560–567 (2001). https://doi.org/10.1007/BF03160302

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03160302

Key words

CLC number

Search

Navigation