Abstract
This paper discusses four dynamic optimization problems on an infinite continuous time interval from a viewpoint of Golden optimality. The problem is whether an optimal policy is Golden or not. We solve two control processes with quadratic cost criterion and two allocation processes with discounted square-root reward criterion. Both processes have a linear dynamics. It is shown that one cotrol process does not admit a Golden optimal policy. The other three processes have a Golden optimal policy. Further we illustrate the Golden optimal trajectories through three approaches: (i) one-parametric method, (ii) Euler equation and (iii) Bellman equation.
This is a preview of subscription content, log in via an institution to check access.
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
Bellman, R.E.: Dynamic Programming. Princeton University Press, NJ 1957
Bellman, R.E.: Introduction of the Mathematical Theory of Control Processes, vol. 1, Linear Equations and Quadratic Criteria; vol. 2, Nonlinear Processes. Academic Press, New York 1967; 1971
Bellman, R.E.: Methods of Nonlinear Analysis, vol. 1, vol. 2, Academic Press, New York 1969, 1972
Beutelspacher, A., Petri, B.: Der Goldene Schnitt 2., überarbeitete und erweiterte Auflange. Elsevier GmbH, Spectrum Akademischer, Heidelberg 1996
Dunlap, R.A.: The Golden Ratio and Fibonacci Numbers (Original). World Scientific, Singapore 1977
Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Prentice-Hall, Englewood Cliffs 1963
Iwamoto, S.: Theory of Dynamic Program: Japanese. Khushu University Press, Fukuoka 1987
Iwamoto, S.: Cross dual on the Golden optimum solutions, Mathematical Economics, Kyoto University RIMS Koukyuroku, vol. 1443, pp 27–43, July 2005
Iwamoto, S.: The Golden optimum solution in quadratic programming. In: Takahashi, W., Tanaka, T. (eds) Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis (Okinawa, 2005). Yokohama Publishers, Yokohama, pp. 199–205, 2007
Iwamoto, S.: The Golden trinity — optimility, inequality, identity. Mathematical Economics, Kyoto University RIMS Koukyuroku, vol. 1488, pp 1–14, May 2006
Iwamoto, S., Yasuda, M.: Dynamic programming creates the Golden Ratio, too. In: Proceedings of the 6th International Conference on Optimization: Techniques and Applications (ICOTA 2004), Ballarat, Australia, December 2004
Phelps, E.S.: The Golden rule of accumulation: A fable for growthmen. Am. Econ. Rev. 51, 638–643 (1961)
Walser, H.: Der Goldene Schnitt. B.G. Teubner, Leibzig 1996
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this chapter
Cite this chapter
Iwamoto, S. (2007). Golden optimal policy in calculus of variation and dynamic programming. In: Kusuoka, S., Yamazaki, A. (eds) Advances in Mathematical Economics. Advances in Mathematical Economics, vol 10. Springer, Tokyo. https://doi.org/10.1007/978-4-431-72761-3_4
Download citation
DOI: https://doi.org/10.1007/978-4-431-72761-3_4
Received:
Revised:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-72733-0
Online ISBN: 978-4-431-72761-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)