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A Concise Guide to Dynamic Optimization

43 Pages Posted: 16 Oct 2011 Last revised: 27 Nov 2016

Winston W. Chang

State University of New York at Buffalo - Department of Economics

Date Written: November 25, 2016


This paper provides a concise guide to dynamic optimization with an integral treatment on various optimal control and dynamic programming problems. It presents essential theorems and methods for obtaining and characterizing solutions to these problems. The paper discusses Pontryagin's maximum principle in optimal control theory under infinite-time horizon and fixed and variable finite-time horizons, discounting vs. no discounting, discrete- vs. continuous-time cases, and the classical calculus of variations method. It also discusses Bellman's principle of optimality in dynamic programming and its relation to the maximum principle. Some elements of stochastic dynamic programming are also discussed.

Keywords: Dynamic optimization, optimal control theory, dynamic programing, Pontryagin's maximum principle, Bellman's principle of optimality, stochastic dynamic programming

JEL Classification: A2, C02, C61, C65, D9

Suggested Citation

Chang, Winston W., A Concise Guide to Dynamic Optimization (November 25, 2016). Available at SSRN: or

Winston W. Chang (Contact Author)

State University of New York at Buffalo - Department of Economics ( email )

453 Fronczak Hall
Department of Economics, SUNY at Buffalo
Buffalo, NY 14260
United States
716-645-8671 (Phone)
716-645-2127 (Fax)


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