On proper minimality in set optimization

The 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 the...

Descripción completa

Detalles Bibliográficos
Autores: Huerga Pastor, Lidia, Miglierina, Enrico, Molho, Elena, Novo, Vicente
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/23985
Acceso en línea:https://hdl.handle.net/20.500.14468/23985
Access Level:acceso abierto
Palabra clave:12 Matemáticas
set optimization
henig proper minimality
geofrion proper minimality
nonlinear scalarization
Descripción
Sumario:The 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.