Shapley–Folkman-type theorem for integrally convex sets
The Shapley–Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex sets, M ♮ -convex sets, and L ♮ -convex sets, which are major classes of discrete convex sets in discrete convex analysis.
Authors
- Kazuo Murota (ORCID: https://orcid.org/0000-0003-1518-9152)
- Akihisa Tamura (ORCID: https://orcid.org/0000-0001-9528-7582)
Institutions
- Keio University (JP)
- The Institute of Statistical Mathematics (JP)
- Tokyo Metropolitan University (JP)
Publication Details
- Journal
- Discrete Applied Mathematics
- Published
- 2024-08-31
- DOI
- https://doi.org/10.1016/j.dam.2024.08.015
- Primary Topic
- Optimization and Variational Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministry of Education, Culture, Sports, Science and Technology
- Japan Society for the Promotion of Science
- Exploratory Research for Advanced Technology