On the Bellman equations with varying control

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The value function is presented by minimisation of a cost functional over admissible controls. The associated first order Bellman equations with varying control are treated. It turns out that the value function is a viscosity solution of the Bellman equation and the comparison principle holds, which is an essential tool in obtaining the uniqueness of the viscosity solutions.

Original languageEnglish
Pages (from-to)51-62
Number of pages12
JournalBulletin of the Australian Mathematical Society
Volume53
Issue number1
Publication statusPublished - 1996 Feb 1
Externally publishedYes

Fingerprint

Bellman Equation
Viscosity Solutions
Value Function
Comparison Principle
Uniqueness
First-order
Costs

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the Bellman equations with varying control. / Koike, Shigeaki.

In: Bulletin of the Australian Mathematical Society, Vol. 53, No. 1, 01.02.1996, p. 51-62.

Research output: Contribution to journalArticle

@article{3fd86585fcdc441787c0bce6dd6088b9,
title = "On the Bellman equations with varying control",
abstract = "The value function is presented by minimisation of a cost functional over admissible controls. The associated first order Bellman equations with varying control are treated. It turns out that the value function is a viscosity solution of the Bellman equation and the comparison principle holds, which is an essential tool in obtaining the uniqueness of the viscosity solutions.",
author = "Shigeaki Koike",
year = "1996",
month = "2",
day = "1",
language = "English",
volume = "53",
pages = "51--62",
journal = "Bulletin of the Australian Mathematical Society",
issn = "0004-9727",
publisher = "Cambridge University Press",
number = "1",

}

TY - JOUR

T1 - On the Bellman equations with varying control

AU - Koike, Shigeaki

PY - 1996/2/1

Y1 - 1996/2/1

N2 - The value function is presented by minimisation of a cost functional over admissible controls. The associated first order Bellman equations with varying control are treated. It turns out that the value function is a viscosity solution of the Bellman equation and the comparison principle holds, which is an essential tool in obtaining the uniqueness of the viscosity solutions.

AB - The value function is presented by minimisation of a cost functional over admissible controls. The associated first order Bellman equations with varying control are treated. It turns out that the value function is a viscosity solution of the Bellman equation and the comparison principle holds, which is an essential tool in obtaining the uniqueness of the viscosity solutions.

UR - http://www.scopus.com/inward/record.url?scp=0039926045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039926045&partnerID=8YFLogxK

M3 - Article

VL - 53

SP - 51

EP - 62

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 1

ER -