Abstract
The present paper gives a systematic presentation of different definitions of optimality in the infinite-time optimal control problem. Some of these definitions are new, while others have been used throughout the literature, sometimes with different names. The logical implications between them are clearly stated, corresponding comparison criteria for solutions are defined, and other relations as well as two types of equivalence relations are established.
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References
Pontryagin, L. S., et. al.,The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, New York, 1962.
Ramsey, F. P.,A Mathematical Theory of Savings, Economic Journal, Vol. 38, pp. 543–559, 1928.
Arrow, K., andKurz, M.,Public Investment, the Rate of Return, and Optimal Fiscal Policy, The Johns Hopkins Press, Baltimore, Maryland, 1970.
Gale, D.,On Optimal Development in a Multi-Sector Economy, Review of Economic Studies, Vol. 34, pp. 1–18, 1967.
Halkin, H.,Necessary Conditions for Optimal Control Problems with Infinite Horizons, Econometrica, Vol. 42, pp. 267–272, 1974.
Haurie, A.,Optimal Control on an Infinite Time Horizon: The Turnpike Approach, Journal of Mathematical Economics, Vol. 3, pp. 81–102, 1976.
Seierstad, A., andSydsaeter, K.,Sufficient Conditions in Optimal Control Theory, International Economic Review, Vol. 18, pp. 367–391, 1977.
Von Weizsäcker, C. C.,Existence of Optimal Programs of Accumulation for an Infinite Time Horizon, Review of Economic Studies, Vol. 32, pp. 85–104, 1965.
Stern, L. E.,Transversality Conditions in the Infinite-Horizon Problem, Working Paper, 1983.
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Communicated by L. D. Berkovitz
This work was supported in part by Simmons College Fund for Research, Grant No. 201.
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Stern, L.E. Criteria of optimality in the infinite-time optimal control problem. J Optim Theory Appl 44, 497–508 (1984). https://doi.org/10.1007/BF00935464
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DOI: https://doi.org/10.1007/BF00935464