On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals
type: Item
instance of: scholarly article
title: On the existence of catching-up optimal solutions for Lagrange problems defined on unbounded intervals
zbMATH Open document ID: 0573.49003
DOI: 10.1007/BF00940757
author: Dean A. Carlson
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: We are concerned with the question of the existence of optimal solutions for infinite-horizon optimal control problems of Lagrange type. In such problems, the objective or cost functional is described by an improper integral. As dictated by applications arising in mathematical economics, we do not a priori assume that this improper integral converges. This leads us to consider a weaker type of optimality, known as catching up optimality. The results presented here utilize the classical convexity and seminormality conditions typically imposed in the existence theory for the case of finite intervals. These conditions are significantly weaker than those imposed by other authors; as a consequence, their existence results are contained as special cases of the results presented here. The method of proof utilizes the Carathéodory-Hamilton-Jacobi theory previously developed by the author for infinite-horizon optimal control problems.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 3915064
zbMATH Keywords: infinite-horizon optimal control problems of Lagrange type
zbMATH Keywords: catching up optimality
zbMATH Keywords: existence results
MaRDI profile type: Publication
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cites work: On Existence of Overtaking Optimal Trajectories Over an Infinite Time Horizon
cites work: A note on the existence of an optimal capital accumulation in the continuous time horizon
cites work: Q4743352
cites work: A Carathéodory-Hamilton-Jacobi theory for infinite-horizon optimal control problems
cites work: Existence theorems for Lagrange control problems with unbounded time domain
cites work: An existence result for optimal economic growth problems
cites work: Remarks on some existence theorems for optimal control
cites work: On recent existence theorems in the theory of optimization
description: scientific article; zbMATH DE number 3915064