Some useful set-valued maps in set optimization. (3rd August 2017)

• Record Type: Journal Article
• Authors: Hernández, Elvira; López, Rubén
• Is Part Of: Optimization. Volume 66:Number 8(2017)
• Page Start: 1273
• Page End: 1289
• Publication Date: 2017-08-03
• Subjects: Asymptotic cone and function -- asymptotic map -- set-valued maps -- set optimization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1310211
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this article, we introduce several classes of set-valued maps which can be useful in set optimization due to their applications. Exactly, we present some set-valued maps defined by scalar and vector functions and study their properties such as continuity and convexity among others. In addition, we compute their asymptotic maps which can be employed to establish coercivity and existence results in the framework of set optimization problems. Finally, we expose some possible directions for further research.