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Axiomatic approach to approximate solutions in multiobjective optimization

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Abstract

An axiomatic approach is introduced in order to study the approximate solution map of a vector optimization problem in the image space. We investigate the possibility to formulate an appropriate notion of approximate solutions that is compatible with von Neumann–Morgenstern utility theory. 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 solutions of the problem, or it coincides with the whole admissible set. Moreover, the geometry of the approximate solution map is studied in some special cases.

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Authors and Affiliations

  1. Department of Economics, University of Insubria, via Monte Generoso 71, Varese, 21100, Italy

    E. Miglierina

  2. Department of Management Sciences, University of Pavia, Pavia, Italy

    E. Molho

  3. DIPTEM, University of Genoa, Genoa, Italy

    F. Patrone

  4. CentER and Department of Econometrics and Operations Research, Tilburg University, Tilburg, The Netherlands

    S. H. Tijs

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  1. E. Miglierina
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  2. E. Molho
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  3. F. Patrone
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  4. S. H. Tijs
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Correspondence to E. Miglierina.

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Miglierina, E., Molho, E., Patrone, F. et al. Axiomatic approach to approximate solutions in multiobjective optimization. Decisions Econ Finan 31, 95–115 (2008). https://doi.org/10.1007/s10203-008-0080-5

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  • DOI: https://doi.org/10.1007/s10203-008-0080-5

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