Parameterization and graphic aid in gradient methods

  • Jean-Pierre Peltier
Numerical Methods
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3)


The first part reports an experiment in which a graphic interactive console was used to operate a gradient-type optimization program.

Some indications are provided on the program sturcture and the requirements for the graphic software. Conclusions are drawn both upon advantages and difficulties related to such project.

The second part deals with parameterization of optimal control problems (i.e. solution through non-linear programming). A local measure of the loss of freedom pertaining to such technique is established. Minimization of this loss leads to the concept of optimal parameterization. A first result is given and concerns the metric in parameters space.


Optimal Control Problem Memory Block Design Vector Past Step Monitor Option 
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.


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Part 1

  1. FAVE, J. — Critère de convergence par approximation de l'optimum pour la méthode du gradient, in computing methods in optimization problems, springer verlag 1969, p. 101–113 (proceedings of the 2nd International Conference on Computational methods and optimization problems, San Remo, sept. 1968).Google Scholar
  2. KELLEY, H.J. — Methods of gradients in Optimization Techniques, G. Leitmann ed., Ac. Press, 1962, p. 248–251.Google Scholar
  3. STEPNIEWSKI, W.Z., KALMBACH, C.F. Jr. — Multivariable search and its application to aircraft design optimization. The Boeing Company, Vertol division, 1969.Google Scholar

Part 2

  1. BRUSCH, R.G., SCHAPPELLE, R.H. — Solution of highly constrained optimal control problems using non-linear programming. AIAA paper 70-964 and AIAA Journal, vol. 11 no 2, p. 135–136.Google Scholar
  2. CULLUM Jane — Finite dimensional approximations of state constrained continuous optimal control problems. SIAM J. Control, vol. 10 no 4, Nov. 1972, p. 649–670.CrossRefGoogle Scholar
  3. JOHNSON, I.L., KAMM, J.L. — Near optimal shuttle trajectories using accelerated gradient methods AAS/AIAA paper 328. Astrodynamics specialists conference, August 17–19 1971, Fort Landerdale Florida.Google Scholar
  4. KELLEY, H.J., DENHAM, W.F. — Modeling and adjoint for continuous systems 2nd International Conference on Computing Methods in Optimization Problems, San Remo, Italy, 1968 and JOTA vol. 3, no 3, p. 174–183.Google Scholar
  5. PIGOTT, B.A.M. — The solution of optimal control problems by function minimization methods. RAE Technical Report 71149, July 1971.Google Scholar
  6. SPEYER, J.L., KELLEY, H.J., LEVINE, N., DENHAM, W.F. — Accelerated gradient projection technique with application to rocket trajectory optimization. Automatica, vol. 7, p. 37–43, 1971.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • Jean-Pierre Peltier
    • 1
  1. 1.Office National d'Etudes et de Recherches Aérospatiales (ONERA)ChâtillonFrance

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