An alternative theorem for set-valued maps via set relations and its application to robustness of feasible sets
Yuto Ogata, Tamaki Tanaka, Yutaka Saito, Gue Myung Lee, Jae‐Hyoung Lee · Optimization · 2018
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.