This work focuses on scalarization processes for nonconvex set-valued optimization problems whose solutions are defined by the socalled l-type less order relation, the final space is normed and the ordering cone is not necessarily solid. A scalarization mapping is introduced, which generalizes the well-known oriented distance, and its main properties are stated. In particular, by choosing a suitable norm it is shown that it coincides with the generalization of the so-called Tammer-Weidner nonlinear separation mapping to this kind of optimization problems. After that, two concepts of solution are characterized in terms of solutions of associated scalar optimization problems defined through the new scalarization mapping.

Gutiérrez, C., Jiménez, B., Miglierina, E., Molho, E., Scalarization of Set-Valued Optimization Problems in Normed Spaces, in Le, T. H. A., Pham, D. T., Nguyen, N. T. (ed.), Modelling, Computation and Optimization in Information Systems and Management Sciences, Springer, Cham 2015: <<ADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING>>, 359 505- 512. 10.1007/978-3-319-18161-5_43 [http://hdl.handle.net/10807/70318]

Scalarization of Set-Valued Optimization Problems in Normed Spaces

Miglierina, Enrico;
2015

Abstract

This work focuses on scalarization processes for nonconvex set-valued optimization problems whose solutions are defined by the socalled l-type less order relation, the final space is normed and the ordering cone is not necessarily solid. A scalarization mapping is introduced, which generalizes the well-known oriented distance, and its main properties are stated. In particular, by choosing a suitable norm it is shown that it coincides with the generalization of the so-called Tammer-Weidner nonlinear separation mapping to this kind of optimization problems. After that, two concepts of solution are characterized in terms of solutions of associated scalar optimization problems defined through the new scalarization mapping.
Inglese
Modelling, Computation and Optimization in Information Systems and Management Sciences
978-3-319-18160-8
359
Gutiérrez, C., Jiménez, B., Miglierina, E., Molho, E., Scalarization of Set-Valued Optimization Problems in Normed Spaces, in Le, T. H. A., Pham, D. T., Nguyen, N. T. (ed.), Modelling, Computation and Optimization in Information Systems and Management Sciences, Springer, Cham 2015: <<ADVANCES IN INTELLIGENT SYSTEMS AND COMPUTING>>, 359 505- 512. 10.1007/978-3-319-18161-5_43 [http://hdl.handle.net/10807/70318]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/70318
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact