Scalarization of Levitin–Polyak well-posed set optimization problems. (2nd January 2017)

• Record Type: Journal Article
• Authors: Khoshkhabar-amiranloo, S.; Khorram, E.
• Is Part Of: Optimization. Volume 66:Number 1(2017)
• Page Start: 113
• Page End: 127
• Publication Date: 2017-01-02
• Subjects: Levitin–Polyak well-posedness -- metrically well-setness -- set optimization -- scalarization functions -- point-to-set distance; 80M50 -- 49K40 -- 54C60; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1253086
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: The aim of this paper is to study Levitin–Polyak ( LP in short) well-posedness for set optimization problems. We define the global notions of metrically well-setness and metrically LP well-setness and the pointwise notions of LP well-posedness, strongly DH-well-posedness and strongly B-well-posedness for set optimization problems. Using a scalarization function defined by means of the point-to-set distance, we characterize the LP well-posedness and the metrically well-setness of a set optimization problem through the LP well-posedness and the metrically well-setness of a scalar optimization problem, respectively.