Treatment of set order relations by means of a nonlinear scalarization functional: a full characterization |
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Authors: | Elisabeth Köbis Markus A Köbis |
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Institution: | 1. Faculty of Natural Sciences II, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germany.elisabeth.koebis@mathematik.uni-halle.de;3. Faculty of Natural Sciences II, Institute of Mathematics, Martin-Luther-University Halle-Wittenberg, Halle, Germany. |
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Abstract: | In this paper, we show how a nonlinear scalarization functional can be used in order to characterize several well-known set order relations and which thus plays a key role in set optimization. By means of this functional, we derive characterizations for minimal elements of set-valued optimization problems using a set approach. Our methods do not rely on any convexity assumptions on the considered sets. Furthermore, we develop a derivative-free descent method for set optimization problems without convexity assumptions to verify the usefulness of our results. |
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Keywords: | Set optimization set order relations nonlinear scalarizing functional descent method |
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