Dynamic Optimization

Jean-Pierre Corriou
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Jean-Pierre Corriou: University of Lorraine

Chapter Chapter 12 in Numerical Methods and Optimization, 2021, pp 653-708 from Springer

Abstract: Abstract Dynamic optimization deals with problems where the solution depends on time or space. It is exposed under different angles. First, from a purely mathematical point of view, the problem is solved based on variational calculus. First order Euler conditions are demonstrated, and second order Legendre–Clebsch are mentioned. The same problem is discussed using Hamilton–Jacobi framework. Then, dynamic optimization in continuous time is treated in the framework of optimal control. Successively, Euler’s method, Hamilton–Jacobi, and Pontryagin’s maximum principle are exposed. Several detailed examples accompany the different techniques. Numerical issues with different solutions are explained. The continuous-time part is followed by the discrete-time part, i.e. dynamic programming. Bellman’s theory is explained both by backward and forward induction with clear numerical examples.

Date: 2021
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DOI: 10.1007/978-3-030-89366-8_12

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