Robustness of feasibility for multi-valued optimization via sublinear characterization (Study on Nonlinear Analysis and Convex Analysis)

Abstract

This paper contains Gordan type theorems of the alternative based on set relations and some robustness of feasibility for multi-valued optimization problems. Gordan's theorem of the alternative standing on the convex separation theorem has shown the duality of linear functions. We investigate generalized ones of Gordan's and they are introduced by a non-linear separation so that they omit the linearity and the convexity from their assumptions.