An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets

作者：Ogata Yuto^*; Tanaka Tamaki; Saito Yutaka; Lee Gue Myung; Lee Jae Hyoung

来源：Optimization, 2018, 67(7): 1067-1075.

DOI：10.1080/02331934.2018.1426582

• Alternative theorem
• set-valued map
• set relation
• evaluation function
• robustness

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.

• 出版日期2018