A Hausdorff-type distance, the Clarke generalized directional derivative and applications in set optimization problems. Issue 4 (4th March 2022)

• Record Type: Journal Article
• Authors: Han, Yu
• Is Part Of: Applicable analysis. Volume 101:Issue 4(2022)
• Page Start: 1243
• Page End: 1260
• Publication Date: 2022-03-04
• Subjects: Set optimization problem -- nonlinear scalarizing function -- Hausdorff-type distance -- Clarke generalized directional derivative; 49J53 -- 90C29; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1778673
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this paper, we introduce a Hausdorff-type distance relative to an ordering cone between two sets. We obtain some properties of the Hausdorff-type distance. In particular, we give a characterization of the Hausdorff-type distance. Moreover, we introduce the Clarke generalized directional derivative for set-valued mappings by using the nonlinear scalarizing function for l -type less order relation, which is introduced by Hernández and Rodríguez-Marín [Nonconvex scalarization in set optimization with set-valued maps. J Math Anal Appl. 2007;325:1–18]. Some properties of the Clarke generalized directional derivative are given. As applications, we present necessary and sufficient optimality conditions for set optimization problems.