Ararat, Ç orcid.org/0000-0002-6985-7665 (2026) Set-valued convex compositions. Mathematical Methods of Operations Research. ISSN: 1432-2994
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.
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| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Keywords: | Complete lattice; Set-valued function; Convex function; Composition; Conjugation; Fenchel-Moreau theorem |
| Dates: |
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) |
| Date Deposited: | 03 Jun 2026 09:35 |
| Last Modified: | 03 Jun 2026 09:35 |
| Published Version: | https://link.springer.com/article/10.1007/s00186-0... |
| Status: | Published online |
| Publisher: | Springer |
| Identification Number: | 10.1007/s00186-026-00922-w |
| Related URLs: | |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:241614 |

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