Duality for optimal control-approximation problems with gauges
type: Item
instance of: scholarly article
title: Duality for optimal control-approximation problems with gauges
zbMATH Open document ID: 1016.90076
DOI: 10.4171/ZAA/894
author: U. Krallert
author: Gert Wanka
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2000-02-28T00:00:00Z
full work available at URL: https://eudml.org/doc/50181
review text: Summary: Looking for \(m\) state variables and \(n\) control variables such that the sum of the distance functions between the state variables and the control variables becomes minimal is called control-approximation problem. This problem is investigated under constraints. Moreover, the distances between the control variables themselves are taken into account. Powers of several gauges are chosen as distance functions. The considerations happen in Hausdorff locally convex topological real vector spaces. In particular, location problems of very general type (e.g. so-called multifacility problems) turn out to be special cases of such control-approximation problems. After the formulation of the primal control-approximation problem some considerations con- cerning gauges follow. Then a dual problem is given and weak and strong duality assertions are obtained.
Mathematics Subject Classification ID: 90C46
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90B85
zbMATH DE Number: 1331711
zbMATH Keywords: control-approximation problem
zbMATH Keywords: location problems
zbMATH Keywords: multifacility problems
zbMATH Keywords: gauges
zbMATH Keywords: weak and strong duality
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1331711