Superlinear functionals are used to separate points from a radiant set according to both a strict and a weak version. Strict separation characterizes closed radiant sets; weak separation is used to define evenly radiant sets, which are characterized by means of a property of the tangent cone to the set at points of the boundary. The separation properties can be described via a polarity relation between a normed space X and the set L of continuous superlinear functionals defined on X. Radiant functions are the ones which are increasing along rays, i.e. the ones whose lower level sets are radiant and so they extend the class of quasiconvex functions with minimum at the origin. We study two particular subclasses: the one of l.s.c. radiant functions, whose lower level sets are closed and radiant and the one of evenly radiant functions, whose lower levels are evenly radiant. We introduce a conjugate function (defined on L), in two different versions, and prove the coincidence between a function and its second conjugate when the function belongs to one of the classes mentioned above. The conjugate function is then used to give global optimality conditions for problems described by radiant objective and constraints.

Superlinear separation and dual properties of radiant functions / Zaffaroni, Alberto. - In: PACIFIC JOURNAL OF OPTIMIZATION. - ISSN 1348-9151. - STAMPA. - 2:(2006), pp. 181-202.

Superlinear separation and dual properties of radiant functions

ZAFFARONI, Alberto
2006

Abstract

Superlinear functionals are used to separate points from a radiant set according to both a strict and a weak version. Strict separation characterizes closed radiant sets; weak separation is used to define evenly radiant sets, which are characterized by means of a property of the tangent cone to the set at points of the boundary. The separation properties can be described via a polarity relation between a normed space X and the set L of continuous superlinear functionals defined on X. Radiant functions are the ones which are increasing along rays, i.e. the ones whose lower level sets are radiant and so they extend the class of quasiconvex functions with minimum at the origin. We study two particular subclasses: the one of l.s.c. radiant functions, whose lower level sets are closed and radiant and the one of evenly radiant functions, whose lower levels are evenly radiant. We introduce a conjugate function (defined on L), in two different versions, and prove the coincidence between a function and its second conjugate when the function belongs to one of the classes mentioned above. The conjugate function is then used to give global optimality conditions for problems described by radiant objective and constraints.
2
181
202
Superlinear separation and dual properties of radiant functions / Zaffaroni, Alberto. - In: PACIFIC JOURNAL OF OPTIMIZATION. - ISSN 1348-9151. - STAMPA. - 2:(2006), pp. 181-202.
Zaffaroni, Alberto
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/709384
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact