Huerga Pastor, LidiaMiglierina, EnricoMolho, ElenaNovo, Vicente2024-10-102024-10-102023Huerga, L., Miglierina, E., Molho, E., .; Novo, V. On proper minimality in set optimization. Optimization Letters 18, 513–528 (2024). https://doi.org/10.1007/s11590-023-02005-91862-4472 | eISSN 1862-4480https://doi.org/10.1007/s11590-023-02005-9https://hdl.handle.net/20.500.14468/23985The registered version of this article, first published in “Optim Lett 18, 513–528 (2024", is available online at the publisher's website: Springer, https://doi.org/10.1007/s11590-023-02005-9 La versión registrada de este artículo, publicado por primera vez en “Optim Lett 18, 513–528 (2024", está disponible en línea en el sitio web del editor: Springer, https://doi.org/10.1007/s11590-023-02005-9The aim of this paper is to extend some notions of proper minimality from vector optimization to set optimization. In particular, we focus our attention on the concepts of Henig and Geoffrion proper minimality, which are well-known in vector optimization. We introduce a generalization of both of them in set optimization with finite dimensional spaces, by considering also a special class of polyhedral ordering cone. In this framework, we prove that these two notions are equivalent, as it happens in the vector optimization context, where this property is well-known. Then, we study a characterization of these proper minimal points through nonlinear scalarization, without considering convexity hypotheses.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículoset optimizationhenig proper minimalitygeofrion proper minimalitynonlinear scalarization