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.
Miglierina, E., Molho, E., Patrone, F., Tijs S, H., An axiomatic approach to approximate solutions in multiobjective optimization, <<DECISIONS IN ECONOMICS AND FINANCE>>, 2008; 31 (2): 95-115. [doi:10.1007/s10203-008-0080-5] [http://dx.medra.org/10.1007/s10203-008-0080-5] [http://hdl.handle.net/10807/1431]
An axiomatic approach to approximate solutions in multiobjective optimization
Miglierina, Enrico;
2008
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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