Abstract
In this chapter we present both necessary conditions and sufficient conditions for optimality. These conditions are obtained by generalizing the appropriate finite horizon results. In particular we present the Pontryagin Maximum Principle, and its extension to the infinite horizon.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Halkin, Necessary Conditions for Optimal Control Problems with Infinite Horizon, Econometrics, Vol. 42, pp. 267–273, 1974.
L. S. Pontryagin et al ii, The Mathematical Theory of Optimal Processes, J. Wiley 1962.
H. Halkin, Mathematical Foundations of System Optimization, in G. Leitmann edit., Topics in Optimization, Academic Press 1967
A. Blaquiere and G. Leitmann, On the Geometry of Optimal Processes, in G. Leitmann edit., Topics in Optimization, Academic Press 1967.
G. Leitmann, The Calculus of Variations and Optimal Control, Plenum Press 1981.
O. L. Mangasarian, Sufficient Conditions for the Optimal Control of Non-Linear Systems, SIAM Journal on Control, Vol. 4, pp. 139–152, 1966.
K. Arrow, and M. Kurz, See Ref. 7 of Lecture 1.
G. Leitmann and H. Stalford, A Sufficiency Theory for Optimal Control, Journal of Optimization Theory and Applications, Vol. 8, no. 3, 1971.
D. W. Peterson, A sufficient Maximum Principle, IEEE Trans. Autom. Control, Feb. 1971, pp. 85–86.
C. D. Feinstein and D. G. Luenberger, Analysis of the Asymptotic behavior of Optimal Control Trajectories: The implicit Programming Problem, SIAM Journal on Control and Optimization, Vol. 19, no. 5, Sept. 1981, pp. 561–585.
A. Seierstad and K. Sydsaeter, Sufficient Conditions in Optimal Control Theory, Int. Econ. Review, Vol. 18, no. 2, 1977.
Michel, P. Une Démonstration Élémentaire du Principe de Maximum de Pontryagin, Bulletin de Mathématique Economiques, Vol. 14, 1977, pp. 9–23
F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, Inc., 1983.
Additional References
Peterson, D. W. and Zalkind, J. H., A Review of Direct Sufficient Conditions in Optimal Control Theory, International Journal on Control, Vol. 28, no. 4, 1978.
Sethi, S. P. and Thompson, G. L., Optimal control Theory: Management Science Applications, Martinus Nijhoff Pub. Co., Boston, MA, 1981.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Carlson, D.A., Haurie, A. (1987). Necessary Conditions and Sufficient Conditions for Optimality. In: Infinite Horizon Optimal Control. Lecture Notes in Economics and Mathematical Systems, vol 290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02529-1_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-02529-1_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17824-8
Online ISBN: 978-3-662-02529-1
eBook Packages: Springer Book Archive