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Fakultät für Mathematik
Fakultät für Mathematik
U.Krallert; G.Wanka : Efficiency in seminorm location problems

U.Krallert; G.Wanka : Efficiency in seminorm location problems

Author(s) :
U.Krallert; G.Wanka
Title :
Efficiency in seminorm location problems
Electronic source:
Preprint series
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 97-27, 1997
Mathematics Subject Classification :
90B85 [ Continuous location ]
90C29 [ Multi-objective programming, etc. ]
Abstract :
Connections between the solution of a single objective location optimization problem and the efficiency sets of the belonging multiobjective location optimization problem in $\bbR^n$ have already been investigated extensively. In this work connections between efficiency sets of multiobjective location optimization problems and solutions of single objective location optimization problems in Hausdorff locally convex topological vector spaces with seminorms as distance functions are given. If the single objective location optimization problems are replaced by multiobjective location optimization problems, e.g. because several seminorms or even families of seminorms are used simultaneously instead of only one seminorm for the single objective location optimization problem, then the ideal solution of this multiobjective location optimization problems should be considered. Then it is possible to produce a multiobjective location optimization problem which consists of collections of several criteria, e.g. with regard to the several seminorms. For only one seminorm the well-known multiobjective location optimization problem arises as a collection of single criteria. The application of Hilbertian seminorm families introduces the concept of projections. Then relations between efficiency sets, weak efficiency sets and definite sets of projections are shown which are partially generalizations of those by E.Carrizosa, E.Conde, F.R.Fernandez and J.Puerto. Examples explain the results.
Keywords :
multiobjective location, efficiency, seminorm, semiscalar product
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