Image space analysis to lagrange duality in nonconvex set optimization

The main purpose of this paper is to study the Lagrange duality for a nonconvex constrained set optimization problem by virtue of the image space analysis.We consider a set optimization formulation for the dual problem by means of the upper quasi-ordering among sets, and we propose the quasi-interior, the quasi-relative interior, and the linear image regularity conditions to establish the strong duality between the primal problem and dual problem from the analysis in the image space.