Two Set Scalarizations Based on the Oriented Distance with Variable Ordering Structures: Properties and Application to Set Optimization. (23rd August 2021)

• Record Type: Journal Article
• Authors: Jiménez, B.; Novo, V.; Vílchez, A.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 12(2021)
• Page Start: 1367
• Page End: 1392
• Publication Date: 2021-08-23
• Subjects: Set optimization -- scalarization in set optimization -- set order relation -- variable ordering structures -- oriented distance; 06A75 -- 49J53 -- 90C29; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1959345
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We consider two set relations defined by general variable order structures and some of their properties are studied. These set relations are characterized by using two scalarization functions based on the oriented distance introduced by Ansari, Köbis and Sharma (Optimization 67 (2018), no. 9, 1389-1407). For these functions, several properties are investigated such as monotonicity and invariance and, by introducing new concepts of properness and boundedness for a set, their finitude is derived. Finally, in set optimization with set criterion and general variable order structures, minimal solutions are characterized by using the scalarization functions above mentioned. Illustrative examples are also given along the paper.