Projection methods for finding the greatest element of the intersection of max-closed convex sets

Tomáš Dlask ()
Additional contact information
Tomáš Dlask: Faculty of Electrical Engineering, Czech Technical University in Prague

Annals of Operations Research, 2024, vol. 340, issue 2, No 4, 836 pages

Abstract: Abstract We focus on the problem of finding the greatest element of the intersection of max-closed convex sets. For this purpose, we analyze the famous method of cyclic projections and show that, if this method is suitably initialized and applied to max-closed convex sets, it converges to the greatest element of their intersection. Moreover, we propose another projection method, called the decreasing projection, which turns out both theoretically and practically preferable to Euclidean projections in this particular case. Next, we argue that several known algorithms, such as Bellman-Ford and Floyd-Warshall algorithms for shortest paths or Gauss-Seidel variant of value iteration in Markov decision processes, can be interpreted as special cases of iteratively applying decreasing projections onto certain max-closed convex sets. Finally, we link decreasing projections (and thus also the aforementioned algorithms) to bounds consistency in constraint programming.

Keywords: Euclidean projection; Max-closed set; Max-closed polyhedron; Shortest paths (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-024-05980-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:340:y:2024:i:2:d:10.1007_s10479-024-05980-z

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-024-05980-z

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().