Skip to main content
Log in

Two methods for large-scale nonlinear optimization and their comparison on a case study of hydropower optimization

  • Contributed Papers
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper presents two methods for the optimization of structured large-scale problems: a decomposition method of dual type for nonlinear problems and a sequential quadratic programming based method. Practical details of application of the methods to the case study problem of the hydropower system of an African river are then given. Comparison of results is presented, indicating that both methods are useful and efficient, having however different features from a practical point of view. General remarks concerning the practical differences between a decomposition-based method and a method exploiting the problem structure within the framework of general purpose optimization routines are finally presented.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Grygier, J. C., andStedinger, J. R.,Algorithms for Optimizing Hydropower System Operation, Water Resources Research, Vol. 21, No. 1, pp. 1–10, 1985.

    Google Scholar 

  2. Soliman, S. A., andChristensen, G. S.,Optimization of Hydropower Systems: Operation with a Quadratic Model, Automatica, Vol. 24, No. 2, pp. 249–256, 1988.

    Article  MathSciNet  Google Scholar 

  3. Yeh, W. W. G.,Reservoir Management and Operations Models: A State of the Art Review, Water Resources Research, Vol. 21, No. 12, pp. 1797–1818, 1985.

    Google Scholar 

  4. Haimes, Y. Y.,Hierarchical Analysis of Water Resources Systems, McGraw-Hill, New York, New York, 1977.

    Google Scholar 

  5. Tatjewski, P.,New Dual-Type Decomposition Algorithm for Nonconvex Separable Optimization Problems, Automatica, Vol. 25, No. 2, pp. 233–242, 1989.

    Article  Google Scholar 

  6. Malinowski, K., Tatjewski, P. andWołochowicz, P.,Development and Implementation of Optimization Techniques and Balancing Functions for Decision Support Systems, Water Resource Management of Multiple Reservoirs, Technical Report, Institute of Automatic Control, Warsaw University of Technology, Warsaw, Poland, 1989.

    Google Scholar 

  7. Fletcher, R.,Practical Methods of Optimization, Vol. 2: Constrained Optimization, Wiley, Chichester, England, 1981.

    Google Scholar 

  8. Powell, M. J. D.,A Fast Algorithm for Nonlinearly Constrained Optimization Calculations, Numerical Analysis, Dundee 1977; Edited by G. A. Watson, Springer, Berlin, Germany, 1978.

    Google Scholar 

  9. Schittkowski, K.,Nonlinear Programming Codes: Information, Test, Performance, Springer, Berlin, Germany, 1980.

    Google Scholar 

  10. Arnold, E.,Zur optimalen Steuerung zeitdiskreter dynamischer Prozesse mittels nichtlinearer Optimierung mit Anwendungen auf die Klimasteuerung von Gewächshäusern, PhD Thesis, Illmenau Institute of Technology, Ilmenau, Germany, 1987 (in German).

    Google Scholar 

  11. Bertsekas, D. P.,Projected Newton Methods for Optimiziation Problems with Simple Constraints, SIAM Journal on Control and Optimization, Vol. 20, No. 2, pp. 221–246, 1982.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by C. T. Leondes

This work was partly supported by the Water Resource Project, IIASA, Laxenburg, Austria.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arnold, E., Tatjewski, P. & Wołochowicz, P. Two methods for large-scale nonlinear optimization and their comparison on a case study of hydropower optimization. J Optim Theory Appl 81, 221–248 (1994). https://doi.org/10.1007/BF02191662

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02191662

Key Words

Navigation