Abstract
A general convergence theorem for gradient algorithms in normed spaces is given and is applied to the unconstrained optimal control problem. A further application is given to time-lag systems of neutral type.
Similar content being viewed by others
References
Glashoff, K.,Die Schrittweite beim Gradientenprojektionsverfahren für Probleme der Optimalen Steuerung, Zeitschrift für Angewandte Matematik und Mechanik, Vol. 51, pp. 445–449, 1971.
Polak, E.,Computational Methods in Optimization: A Unified Approach, Academic Press, New York, New York, 1971.
Leese, S. J.,Fréchet Differentiability and Optimal Control, Loughborough University of Technology, Loughborough, Leicestershire, England, Mathematics Research Report No. 81, 1975.
Daniel, J. W.,The Approximate Minimization of Functionals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.
Goldstein, A. A.,Constructive Real Analysis, Harper and Row Publishers, New York, New York, 1967.
Connor, M. A., andLeese, S. J.,A Gradient Method for Neutral Systems, Journal of Optimization Theory and Applications, Vol. 21, No. 3, 1977.
Polak, E.,An Historical Survey of Computational Methods in Optimal Control, SIAM Review, Vol. 15, pp. 553–584, 1973.
Author information
Authors and Affiliations
Additional information
Communicated by D. Q. Mayne
This work was completed while the author held a Science Research Council Postdoctoral Fellowship at Loughborough University of Technology, Loughborough, Leicestershire, England.
Rights and permissions
About this article
Cite this article
Leese, S.J. Convergence of gradient methods for optimal control problems. J Optim Theory Appl 21, 329–337 (1977). https://doi.org/10.1007/BF00933534
Issue Date:
DOI: https://doi.org/10.1007/BF00933534