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Dynamic Optimization

In: Numerical Methods and Optimization

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  • Jean-Pierre Corriou

    (University of Lorraine)

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.

Suggested Citation

  • Jean-Pierre Corriou, 2021. "Dynamic Optimization," Springer Optimization and Its Applications, in: Numerical Methods and Optimization, chapter 0, pages 653-708, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-89366-8_12
    DOI: 10.1007/978-3-030-89366-8_12
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    References listed on IDEAS

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