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Daniel, James W.

On the convergence of a numerical method for optimal control problems. (English) Zbl 0174.20704

J. Optim. Theory Appl. 4, No. 5, 330-342 (1969).
Summary: Under suitable restrictions, convergence to the solutions of a class of optimal control problems is proved for a method by Rosen in which the differential equations, constraints, and cost functional are discretized, and the resulting mathematical programming problem is solved approximately by a penalty-function approach.
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Cited in 4 Documents

MSC:

65K10 Numerical optimization and variational techniques
65K05 Numerical mathematical programming methods
49M25 Discrete approximations in optimal control

Keywords:

convergence; numerical method; optimal control problems; penalty-function approach
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References:

[1] Warga, J.,Necessary Conditions for a Minimum in a Relaxed Variational Problem, Journal of Mathematical Analysis and Applications, Vol. 4, No. 2, 1962. · Zbl 0102.31802
[2] Rosen, J. B.,Iterative Solution of Nonlinear Optimal Control Problems, SIAM Journal on Control, Vol. 4, No. 1, 1966. · Zbl 0229.49025
[3] Cullum, J.,Discrete Approximations to Continuous Optimal Control Problems, SIAM Journal on Control, Vol. 7, No. 1, 1969. · Zbl 0175.10502
[4] Daniel, J. W.,Approximate Minimization of Functionals, Mathematics of Computation, Vol. 23, No. 107, 1969. · Zbl 0208.42901
[5] Kantorovich, L., andAkhilov, G.,Functional Analysis in Normed Linear Spaces, The MacMillan Company, New York, 1964.
[6] Taylor, A. E.,Introduction to Functional Analysis, John Wiley and Sons, New York, 1961. · Zbl 0104.42803
[7] Levitin, E. S., andPoljak, B. T.,Convergence of Minimizing Sequences in Conditional Extremum Problems, Soviet Mathematics, Vol. 7, No. 5, 1966. · Zbl 0161.07002
[8] Poljak, B. T.,Existence Theorems and Convergence of Minimizing Sequences in Extremum Problems with Restrictions, Soviet Mathematics, Vol. 7, No. 2, 1966. · Zbl 0171.09501
[9] Roxin, E.,The Existence of Optimal Controls, Michigan Mathematical Journal, Vol. 9, No. 1, 1967. · Zbl 0189.46402
[10] Henrici, P.,Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York, 1962. · Zbl 0112.34901
[11] Krasovskii, N. N.,On a Problem in Optimal Control (in Russian), PMM, Vol. 21, 1957.
[12] Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., andMishchenko, E. F.,The Mathematical Theory of Optimal Processes, John Wiley and Sons, New York, 1962.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.