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Upper and Lower bounds for a certain class of constrained variational problems

Published online by Cambridge University Press:  09 April 2009

M. A. Hanson
M. A. Hanson
Affiliation:
Department of Statistics, University of New South Wales.
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Certain optimization problems involving inequality constraints, known as optimal control problems have been extensively studied during recent years especially in relation to the calculation of optimal rocket thrusts and trajectories. A summary of these works is given by Berkovitz [1] who also establishes necessary conditions for the existence of solutions for a wide class of such problems.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 4 , November 1963 , pp. 449 - 453
Copyright
Copyright © Australian Mathematical Society 1963

References

[1]Berkovitz, L. D., Variational Methods in Problems of Control and Programming, Journal of Mathematical Analysis and Applications, 3 (1961), p. 145.CrossRefGoogle Scholar
[2]Bellman, R., Quasi-linearization and Upper and Lower Bounds for Variational Problems, Quarterly of Appl. Maths. 15 (1962), p. 349.CrossRefGoogle Scholar
[3]Nemytskii, V. V. and Stepanov, V. V., Qualitative Theory of Differential Equations, Chap. I Sect. 2–4 (Princeton University Press, 1960).Google Scholar