An axiomatic approach to approximate solutions in vector optimization

Miglierina Enrico, Molho Elena (), Patrone Fioravante () and Steff H. Tijs ()
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Miglierina Enrico: Department of Economics, University of Insubria, Italy
Molho Elena: Department of Management Sciences, University of Pavia
Patrone Fioravante: Department of Mathematics, University of Genoa, Italy
Steff H. Tijs: Department of Econometrics, University of Tilburg, Netherlands

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: In vector optimization many notions of approximate solution have been proposed in the literature. In this paper an axiomatic approach is introduced in order to study the approximate solution map of a vector optimization problem in the image space. An impossibility result is proved in the sense that, whenever all of the axioms are satisfied, either the set of the approximate solutions is a subset of the exact solution of the problem (the weakly efficient frontier), or it coincides with the whole admissible set. Moreover, the geometry of the approximate solution map is studied in the special case of polyhedral ordering cones generated by a base of R. Finally, we study the shape of the approximate solution map under the assumption of weak approximation consistency.

Keywords: vector optimization; approximate solution; axiomatization. (search for similar items in EconPapers)
Pages: 30 pages
Date: 2005-09
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