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U. Krallert; G. Wanka : Duality for optimal Control-Approximation Problems with Gauges

U. Krallert; G. Wanka : Duality for optimal Control-Approximation Problems with Gauges

Author(s) :
U. Krallert; G. Wanka
Title :
Duality for optimal Control-Approximation Problems with Gauges
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-14, 1998
Mathematics Subject Classification :
49N15 [ Duality theory (optimization) ]
90B85 [ Continuous location ]
41A65 [ Abstract approximation theory ]
90C25 [ Convex programming ]
Abstract :
Looking for a new optimal location point for m given location points such that the sum of the distance between the new location point and the given location points becomes minimal is called 1-location median problem. If even n new location points are searched then it arises the n-location median problem.

In this work this n-location median problem whith restrictions is investigated. Powers of severalgauges are chosen as distance fuctions. The consideration happen in Hausdorff locally convex topological real vector spaces.

This generalized location problem can also be interpreted as a control-approximation problem with m state variables and n control variables.

After the formulation of the primal location or control-approximation problem some considerations to the gauges are performed.

Then a dual problem is given. As a relation between the pimal and the dual problem a waek duality assertion follows. With the help of the duality theory of Fenchel and Rockafellar a strong duality assertion can also be derived.

Keywords :
location problem, control-approximation problem, gauge, duality
Language :
english
Publication time :
6/1998