Set-valued convex compositions
Functional Analysis
2023-06-29 v1 Optimization and Control
Abstract
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.
Cite
@article{arxiv.2306.15906,
title = {Set-valued convex compositions},
author = {Çağın Ararat},
journal= {arXiv preprint arXiv:2306.15906},
year = {2023}
}
Comments
18 pages