An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets. (3rd July 2018)

• Record Type: Journal Article
• Authors: Ogata, Yuto; Tanaka, Tamaki; Saito, Yutaka; Lee, Gue Myung; Lee, Jae Hyoung
• Is Part Of: Optimization. Volume 67:Number 7(2018)
• Page Start: 1067
• Page End: 1075
• Publication Date: 2018-07-03
• Subjects: Alternative theorem -- set-valued map -- set relation -- evaluation function -- robustness; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1426582
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: This paper contains a generalized Gordan-type alternative theorem for set-valued maps which characterizes set relations without any convexity assumptions using certain evaluation functions. As a direct consequence and as a good example, we discuss robustness (or stability) of linear programming problems for modelling error. Moreover, this theorem can be utilized for that of general vector optimization problems in special cases due to reformation of the evaluation functions.