The application of gradient algorithms to the optimization of controlled versions of the world 2 model of forrester

  • J. L. de Jong
  • J. W. Dercksen
Human Environments (Energy, World Models)
Part of the Lecture Notes in Computer Science book series (LNCS, volume 40)


Optimal Control Problem Search Direction Conjugate Gradient Method Gradient Algorithm Coupling Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

7. References

  1. BRYSON Jr, A.E. and HO, Y.C. (1969): Applied Optimal Control, Blaisdell Publ. Cy, Waltham, Mass.Google Scholar
  2. BRYSON, Jr. A.E. and DENHAM, W.F. (1962): A Steepest Ascent Method for Solving Optimum Programming Problems. Trans ASME, J.Appl.Mech. 29, pp. 247–259.Google Scholar
  3. BURNS, J.R. and MALONE, D.W. (1974): Optimization Techniques Applied to the Forrester Model of the World, IEEE Trans.Syst.Man.Cybern., SMC-4, pp. 164–172.Google Scholar
  4. CUYPERS, J.G.M. (1973): Two simplified versions of Forrester's model. Automatica, 9, pp. 399–401.Google Scholar
  5. DEKKER, L. and KERCKHOFFS, E.H.J. (1974): Hybrid simulation of a World model, AICA J. 16, nr.4 pp. 10–14.Google Scholar
  6. FORRESTER, J.W. (1971): World Dynamics, Wright-Allen Press Inc., Cambridge, Mass.Google Scholar
  7. JACOBY, S.L.S., KOWALIK, J.S. and PIZZO, J.T. (1972): Iterative methods for nonlinear optimization problems, Prentice Hall, Inc., Englewood Cliffs, N.J.Google Scholar
  8. KELLER, Jr., E.A. and SENGUPTA, J.K. (1973): Relative efficiency of computing optimal growth by conjugate gradient and Davidon methods, Int. J. Systems Sci, 4, pp. 97–120.Google Scholar
  9. KELLEY, J.H. (1962): Methods of Gradients, Ch. 6 of Optimization Techniques. G. Leitmann (Ed.), Academic Press New York, pp. 206–252.Google Scholar
  10. LASDON, L.S., MITTER, S.K. and WAREN, A.D. (1967) The Conjugate Gradient Method for Optimal Control Problems, IEEE Trans. Aut. Contr., AC-12, pp. 132–138.Google Scholar
  11. MEADOWS, D.H. et al. (1972): The Limits to Growth, Universe Books, New York.Google Scholar
  12. MURRAY, W. (ed) (1972): Numerical methods for unconstrained minimization problems, Academic Press, London.Google Scholar
  13. OLSDER, G.J. and STRIJBOS, R.C.W. (1973). World Dynamics, a dynamic optimization study, Annals of Systems Research, 3, pp. 21–37.Google Scholar
  14. PAGUREK, B. and WOODSIDE, C.M. (1968): The conjugate gradient method for optimal control problems with bounded control variables. Automatica, 4, pp. 337–349.Google Scholar
  15. PIERSON, B.L. and RAJTORA, S.G. (1970): Computational Experience with the Davidon Method Applied to Optimal Control Problems, IEEE Trans Syst. Sci and Cybern., SSC-6, pp. 240–242.Google Scholar
  16. QUINTANA, V.H. and DAVISON, E.J. (1974). Clipping-off gradient algorithms to compute optimal controls with constrained magnitude, Int. J. Control, 20, pp. 245–255.Google Scholar
  17. RADEMAKER, O. (1972): Project Group Global Dynamics, Progress Reports nrs. 1,2 (1972), 3,4 (1974). Available from author, Address: T.H.E., P.O.Box 513, Eindhoven, The Netherlands.Google Scholar
  18. SINNOTT, J.F. and LUENBERGER, D.G. (1967): Solution of Optimal Control Problems by the Method of Conjugate Gradients. JACC 1967 Preprints, pp. 566–574.Google Scholar
  19. TRIPATHI, S.S. and NARENDRA, K.S. (1968): Conjugate direction methods for nonlinear optimization problems, Proc. 1968 NEC (Chicago, Ill.), pp. 125–129.Google Scholar
  20. WONG, P.J., DRESSLER, R.M. and LUENBERGER, D.G. (1971): A combined Parallel-Tangents/Penalty-Function Approach to Solving Trajectory Optimization Problems, AIAAJ 9, pp. 2443–2448.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • J. L. de Jong
    • 1
  • J. W. Dercksen
    • 2
  1. 1.Department of MathematicsEindhoven University of TechnologyThe Netherlands
  2. 2.Netherlands Organization for the Advancement of Pure Research (Z.W.O.) Department of PhysicsEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations