Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization
- Author(s)
- Immanuel Bomze, Michael Kahr, Markus Leitner
- Abstract
We consider the robust standard quadratic optimization problem (RStQP), in which an uncertain (possibly indefinite) quadratic form is optimized over the standard simplex. Following most approaches, we model the uncertainty sets by balls, polyhedra, or spectrahedra, more generally, by ellipsoids or order intervals intersected with subcones of the copositive matrix cone. We show that the copositive relaxation gap of the RStQP equals the minimax gap under some mild assumptions on the curvature of the aforementioned uncertainty sets and present conditions under which the RStQP reduces to the standard quadratic optimization problem. These conditions also ensure that the copositive relaxation of an RStQP is exact. The theoretical findings are accompanied by the results of computational experiments for a specific application from the domain of graph clustering, more precisely, community detection in (social) networks. The results indicate that the cardinality of communities tend to increase for ellipsoidal uncertainty sets and to decrease for spectrahedral uncertainty sets.
- Organisation(s)
- Department of Statistics and Operations Research, Research Network Data Science, Research Platform Governance of digital practices
- External organisation(s)
- Vrije Universiteit Amsterdam
- Journal
- Mathematics of Operations Research
- Volume
- 46
- Pages
- 301-316
- No. of pages
- 16
- ISSN
- 0364-765X
- DOI
- https://doi.org/10.1287/moor.2020.1057
- Publication date
- 09-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101015 Operations research
- Keywords
- ASJC Scopus subject areas
- General Mathematics, Computer Science Applications, Management Science and Operations Research
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/80df4c0d-b2cd-4dfb-9b4f-ed396e3b25c7