2023/06/28 by Ararat, Çağın
#06B23 #26E25 #46A55 #49J53 #90C48 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2306.15906
We study the composition of two set-valued functions defined on locally convex topological linear spaces. We assume that these functions map into certain complete lattices of sets that have been used to establish a conjugation theory for set-valued functions in the literature. Our main result is a formula for the conjugate of the composition in terms of the conjugates of the ingredient functions. As a special case, when the composition is proper and has further regularity, our formula yields a dual representation for the composition. The proof of the main result uses Lagrange duality and minimax theory in a nontrivial way.