Fenchel duality and smoothness of solution of the optimal routing problem
type: Item
instance of: scholarly article
title: Fenchel duality and smoothness of solution of the optimal routing problem
zbMATH Open document ID: 0598.90037
DOI: 10.1016/0005-1098(86)90108-1
author: G. I. Stassinopoulos
published in: Automatica
publication date: 1986-01-01T00:00:00Z
review text: A particular dynamic, linear state and control constrained optimization problem arising in optimal routing in communication networks is investigated by Fenchel duality methods. The original problem is shown to reduce to a finite dimensional dual program having a fairly simple solution. In particular, it is shown that an optimal solution always exists having the following property: all state trajectory components have constant slopes until they switch to zero, whenever the corresponding component hits the boundary. Implications of the main results for the development of on-line solution algorithms are discussed and possible extensions are outlined. The paper concentrates on aspects interesting to control theorists and gives references including important extensions of communication network applications.
reviewed by: Markos Papageorgiou
Mathematics Subject Classification ID: 90B10
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 68M20
zbMATH DE Number: 3965790
zbMATH Keywords: traffic control
zbMATH Keywords: duality
zbMATH Keywords: optimal routing
zbMATH Keywords: communication networks
zbMATH Keywords: Fenchel duality
zbMATH Keywords: on-line solution algorithms
MaRDI profile type: Publication
full work available at URL: 0005-1098(86)90108-1
OpenAlex ID: W2093042386
cites work: Optimal dynamic routing in communication networks with continuous traffic
cites work: Functional analysis and time optimal control
cites work: On Optimal Control Problems with Bounded State Variables and Control Appearing Linearly
cites work: An optimal control approach to dynamic routing in networks
cites work: Duality and stability in extremum problems involving convex functions
cites work: On decentralized dynamic routing for congested traffic networks
cites work: The Modeling of Adaptive Routing in Data-Communication Networks
cites work: Optimal Congestion Control in Single Destination Networks
cites work: Maximal flow through a domain
cites work: Application of duality theory to a class of composite cost control problems
cites work: Q5667133
description: scientific article; zbMATH DE number 3965790