Solvability and algorithms for functional equations originating from dynamic programming
type: Item
instance of: scholarly article
title: Solvability and algorithms for functional equations originating from dynamic programming
zbMATH Open document ID: 1232.39024
DOI: 10.1155/2011/701519
author: Guo-Jing Jiang
author: Shin Min Kang
author: Young Chel Kwun
published in: Fixed Point Theory and Applications
publication date: 2011-05-19T00:00:00Z
full work available at URL: https://eudml.org/doc/224440
review text: The purpose of the paper is to study the functional equation \[ f(x)=\text{opt}_{y\in D}\text{opt}\{p(x,y),q(x,y)f(a(x,y)),r(x,y)f(b(x,y)),s(x,y)f(c(x,y))\}, \] where the operator ``\(\text{opt}\)'' may stand for any of \(\sup,\inf,\max,\min\). This equation arises in dynamic programming of multistage decision processes. Using the Banach fixed point theorem as a main tool, existence and uniqueness theorems and iterative approximations of the solutions are obtained. Eight nontrivial examples are also discussed.
reviewed by: Zsolt Páles
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 65Q20
zbMATH DE Number: 5897688
zbMATH Keywords: dynamic programming
zbMATH Keywords: multistage decision processes
zbMATH Keywords: functional equation
zbMATH Keywords: iteration
zbMATH Keywords: Banach fixed point theorem
Wikidata QID: Q59266912
MaRDI profile type: Publication
OpenAlex ID: W2116602587
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description: scientific article; zbMATH DE number 5897688