Input optimization for infinite-horizon discounted programs
type: Item
instance of: scholarly article
title: Input optimization for infinite-horizon discounted programs
zbMATH Open document ID: 0644.90097
DOI: 10.1007/BF00941823
author: Adi Ben-Israel
author: Sjur Didrik Flåm
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let V(x) denote the optimal (maximal) value of a discrete time dynamic program, given the initial state x. This paper is concerned with the inverse correspondence \(V^{-1}\) and its infimum \[ I(v)\quad:=\quad \inf _{x}\{x: V(x)\geq v\} \] for discounted, infinite-horizon programs with one-dimensional state space and monotone V(\(\cdot)\). The function I(v), interpreted as the optimal (minimal) input required to achieve v, is computed using dynamic programming recursion (Theorem 3.1) or value iteration (Theorem 3.2). An application to mathematical economics (optimal consumption plan) is given.
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 91B62
zbMATH DE Number: 4051383
zbMATH Keywords: discrete time dynamic program
zbMATH Keywords: discounted infinite-horizon programs
zbMATH Keywords: value iteration
zbMATH Keywords: optimal consumption
zbMATH Keywords: optimality principle
zbMATH Keywords: optimal plans
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00941823
OpenAlex ID: W2053764129
description: scientific article; zbMATH DE number 4051383