On the Euler equation approach to discrete--time nonstationary optimal control problems

David González-Sánchez; Onésimo Hernández-Lerma

doi:10.3934/jdg.2014.1.57

Article Contents

2014, Volume 1, Issue 1: 57-78. Doi: 10.3934/jdg.2014.1.57

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On the Euler equation approach to discrete--time nonstationary optimal control problems

David González-Sánchez^1, and
Onésimo Hernández-Lerma^2,

1.
Departamento de Matemáticas, Instituto Tecnológico Autónomo de México (ITAM), Río Hondo 1, México D.F. 01000
2.
Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000

Received: March 31, 2012

Revised: February 28, 2013

Published: December 2013

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Abstract

We are concerned with deterministic and stochastic nonstationary discrete--time optimal control problems in infinite horizon. We show, using Gâteaux differentials, that the so--called Euler equation and a transversality condition are necessary conditions for optimality. In particular, the transversality condition is obtained in a more general form and under milder hypotheses than in previous works. Sufficient conditions are also provided. We also find closed--form solutions to several (discounted) stationary and nonstationary control problems.

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Mathematics Subject Classification: Primary: 93C55, 91B55, 93E20.

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