Vector equilibrium problems under improvement sets and linear scalarization with stability applications. (1st November 2016)

• Record Type: Journal Article
• Authors: Chen, Chun-Rong; Zuo, Xin; Lu, Fang; Li, Sheng-Jie
• Is Part Of: Optimization methods and software. Volume 31:Number 6(2016)
• Page Start: 1240
• Page End: 1257
• Publication Date: 2016-11-01
• Subjects: improvement set -- scalarization -- vector equilibrium problems -- semicontinuity -- strict pseudomonotonicity; 49K40 -- 90C31 -- 47J20; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1200043
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, for vector equilibrium problems where the ordering relations are defined via improvement sets, linear scalarization characterizations are established, which include the well-known ones for vector optimization problems in the literature as special cases. By applying the obtained results, some continuity (both lower and upper semicontinuities) conclusions of parametric problems with respect to vector equilibria through improvement sets are deduced using scalarization approaches. Several unsolved or interesting problems are also proposed.