Characterizing properties of approximate solutions for optimization problems |
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Authors: | Henk Norde Fioravante Patrone Stef Tijs |
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Affiliation: | a Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands;b Department of Mathematics, Via Dodecaneso 35, University of Genoa, 16146 Genoa, Italy |
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Abstract: | Approximate solutions for optimization problems become of interest if the ‘true’ optimum cannot be found: this may happen for the simple reason that an optimum does not exist or because of the ‘bounded rationality’ (or bounded accuracy) of the optimizer. This paper characterizes several approximate solutions by means of consistency and additional requirements. In particular we consider invariance properties. We prove that, where the domain contains optimization problems without maximum, there is no non-trivial consistent solution satisfying non-emptiness, translation and multiplication invariance. Moreover, we show that the class of ‘satisficing’ solutions is obtained, if the invariance axioms are replaced with Chernoff’s Choice Axiom. |
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Keywords: | Approximate optimization Consistency Invariance properties |
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