A set scalarization function based on the oriented distance and relations with other set scalarizations. (2nd December 2018)

• Record Type: Journal Article
• Authors: Jiménez, B.; Novo, V.; Vílchez, A.
• Is Part Of: Optimization. Volume 67:Number 12(2018)
• Page Start: 2091
• Page End: 2116
• Publication Date: 2018-12-02
• Subjects: Scalarization in set optimization -- oriented distance -- set optimization -- set order relations; 06A75 -- 49J53 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1533554
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The aim of this paper is, in the setting of normed spaces with a cone K non necessarily solid, to study new relations among set scalarization functions that are extensions of the oriented distance of Hiriart-Urruty. Moreover, we deal with a set scalarization function of sup-inf type, we investigate its relation to the cone-properness and cone-boundedness and it is related to other set scalarizations existing in the literature. In particular, with the norm induced by the Minkowski's functional, we obtain relations with a set scalarization which is an extension of the so called Gerstewitz's scalarization function.