Value function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Value function" in English language version.

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Fleming, Wendell H.; Rishel, Raymond W. (1975). Deterministic and Stochastic Optimal Control. New York: Springer. pp. 81–83. ISBN 0-387-90155-8.
Caputo, Michael R. (2005). Foundations of Dynamic Economic Analysis : Optimal Control Theory and Applications. New York: Cambridge University Press. p. 185. ISBN 0-521-60368-4.
Corbae, Dean; Stinchcombe, Maxwell B.; Zeman, Juraj (2009). An Introduction to Mathematical Analysis for Economic Theory and Econometrics. Princeton University Press. p. 145. ISBN 978-0-691-11867-3.
Ljungqvist, Lars; Sargent, Thomas J. (2018). Recursive Macroeconomic Theory (Fourth ed.). Cambridge: MIT Press. p. 106. ISBN 978-0-262-03866-9.
Kamalapurkar, Rushikesh; Walters, Patrick; Rosenfeld, Joel; Dixon, Warren (2018). "Optimal Control and Lyapunov Stability". Reinforcement Learning for Optimal Feedback Control: A Lyapunov-Based Approach. Berlin: Springer. pp. 26–27. ISBN 978-3-319-78383-3.

Benveniste and Scheinkman established sufficient conditions for the differentiability of the value function, which in turn allows an application of the envelope theorem, see Benveniste, L. M.; Scheinkman, J. A. (1979). "On the Differentiability of the Value Function in Dynamic Models of Economics". Econometrica. 47 (3): 727–732. doi:10.2307/1910417. JSTOR 1910417. Also see Seierstad, Atle (1982). "Differentiability Properties of the Optimal Value Function in Control Theory". Journal of Economic Dynamics and Control. 4: 303–310. doi:10.1016/0165-1889(82)90019-7.
Zhou, X. Y. (1990). "Maximum Principle, Dynamic Programming, and their Connection in Deterministic Control". Journal of Optimization Theory and Applications. 65 (2): 363–373. doi:10.1007/BF01102352. S2CID 122333807.

Benveniste and Scheinkman established sufficient conditions for the differentiability of the value function, which in turn allows an application of the envelope theorem, see Benveniste, L. M.; Scheinkman, J. A. (1979). "On the Differentiability of the Value Function in Dynamic Models of Economics". Econometrica. 47 (3): 727–732. doi:10.2307/1910417. JSTOR 1910417. Also see Seierstad, Atle (1982). "Differentiability Properties of the Optimal Value Function in Control Theory". Journal of Economic Dynamics and Control. 4: 303–310. doi:10.1016/0165-1889(82)90019-7.

Zhou, X. Y. (1990). "Maximum Principle, Dynamic Programming, and their Connection in Deterministic Control". Journal of Optimization Theory and Applications. 65 (2): 363–373. doi:10.1007/BF01102352. S2CID 122333807.