Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 2, pp. 491  504 (1999) 

Duality for Optimal ControlApproximation Problems with GaugesG. Wanka and U. KrallertBoth authors: Techn. Univ., Fak. Math., D09107 ChemnitzAbstract: Looking for {\it m} state variables and {\it n} control variables such that the sum of the distance functions between the state variables and the control variables becomes minimal is called controlapproximation 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. socalled multifacility problems) turn out to be special cases of such controlapproximation problems. After the formulation of the primal controlapproximation problem some considerations concerning gauges follow. Then a dual problem is given and weak and strong duality assertions are obtained. Full text of the article:
Electronic fulltext finalized on: 31 Jul 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
