A contraction approach to dynamic optimization problems.

An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique sol...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Leif K Sandal, Sturla F Kvamsdal, José M Maroto, Manuel Morán
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/72b5f5e2be5747d8af999c08ed0bb2ff
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:72b5f5e2be5747d8af999c08ed0bb2ff
record_format	dspace
spelling	oai:doaj.org-article:72b5f5e2be5747d8af999c08ed0bb2ff2021-12-02T20:16:17ZA contraction approach to dynamic optimization problems.1932-620310.1371/journal.pone.0260257https://doaj.org/article/72b5f5e2be5747d8af999c08ed0bb2ff2021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0260257https://doaj.org/toc/1932-6203An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions. Solutions are obtained by considering a vector-valued value function and by using an iterative process. Special cases of the general class of contraction problems include the classical Bellman problem and its stochastic formulations. Thus, our approach can be viewed as an extension of the Bellman problem to the special case of nonautonomy that periodicity represents, and our approach thereby facilitates consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization, and furthermore, certain types of dynamic games. The contraction approach is illustrated in simple examples. In the main example, which is an infinite-horizon resource management problem with a periodic price, it is found that the optimal exploitation level differs between high and low price time intervals and that the solution time paths approach a limit cycle.Leif K SandalSturla F KvamsdalJosé M MarotoManuel MoránPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 11, p e0260257 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Leif K Sandal Sturla F Kvamsdal José M Maroto Manuel Morán A contraction approach to dynamic optimization problems.
description	An infinite-horizon, multidimensional optimization problem with arbitrary yet finite periodicity in discrete time is considered. The problem can be posed as a set of coupled equations. It is shown that the problem is a special case of a more general class of contraction problems that have unique solutions. Solutions are obtained by considering a vector-valued value function and by using an iterative process. Special cases of the general class of contraction problems include the classical Bellman problem and its stochastic formulations. Thus, our approach can be viewed as an extension of the Bellman problem to the special case of nonautonomy that periodicity represents, and our approach thereby facilitates consistent and rigorous treatment of, for example, seasonality in discrete, dynamic optimization, and furthermore, certain types of dynamic games. The contraction approach is illustrated in simple examples. In the main example, which is an infinite-horizon resource management problem with a periodic price, it is found that the optimal exploitation level differs between high and low price time intervals and that the solution time paths approach a limit cycle.
format	article
author	Leif K Sandal Sturla F Kvamsdal José M Maroto Manuel Morán
author_facet	Leif K Sandal Sturla F Kvamsdal José M Maroto Manuel Morán
author_sort	Leif K Sandal
title	A contraction approach to dynamic optimization problems.
title_short	A contraction approach to dynamic optimization problems.
title_full	A contraction approach to dynamic optimization problems.
title_fullStr	A contraction approach to dynamic optimization problems.
title_full_unstemmed	A contraction approach to dynamic optimization problems.
title_sort	contraction approach to dynamic optimization problems.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/72b5f5e2be5747d8af999c08ed0bb2ff
work_keys_str_mv	AT leifksandal acontractionapproachtodynamicoptimizationproblems AT sturlafkvamsdal acontractionapproachtodynamicoptimizationproblems AT josemmaroto acontractionapproachtodynamicoptimizationproblems AT manuelmoran acontractionapproachtodynamicoptimizationproblems AT leifksandal contractionapproachtodynamicoptimizationproblems AT sturlafkvamsdal contractionapproachtodynamicoptimizationproblems AT josemmaroto contractionapproachtodynamicoptimizationproblems AT manuelmoran contractionapproachtodynamicoptimizationproblems
_version_	1718374533086314496

A contraction approach to dynamic optimization problems.

Ejemplares similares