Abstract
A general vectorial best approximation problem in linear and locally convex topological spaces, respectively, is considered. The approximation is based on socalled vectorial norms. For efficient, weakly efficient and strongly efficient solutions sufficient optimality conditions which can be interpreted as generalized Kolmogorov-conditions are obtained in vectorial as well as scalarized form.
Zusammenfassung
Untersucht wird ein allgemeines vektorielles Bestapproximationsproblem in linearen bzw. lokalkonvexen topologischen Räumen. Die Approximation wird im Sinne sogenannter vektorieller Normen betrachtet. Es werden für effiziente, schwach effiziente und streng minimale Lösungen hinreichende Optimalitätsbedingungen angegeben. Diese können als verallgemeinerte Kolmogorov Bedingungen interpretiert werden.
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Wanka, G. Kolmogorov-conditions for vectorial approximation problems. OR Spektrum 16, 53–58 (1994). https://doi.org/10.1007/BF01719704
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DOI: https://doi.org/10.1007/BF01719704
Key words
- Vectorial approximation
- optimality conditions
- vectorial norms
- efficient points
- multicriterial optimization