Skip to Main content Skip to Navigation
Journal articles

On the elimination of inessential points in the smallest enclosing ball problem

Abstract : We consider the construction of the smallest ball B * enclosing a set Xn formed by n points in R d. We show that any probability measure on Xn, with mean c and variance matrix V , provides a lower bound b on the distance to c of any point on the boundary of B * , with b having a simple expression in terms of c and V. This inequality permits to remove inessential points from Xn, which do not participate to the definition of B * , and can be used to accelerate algorithms for the construction of B *. We show that this inequality is, in some sense, the best possible. A series of numerical examples indicates that, when d is reasonable small (d ≤ 10, say) and n is large (up to 10 5), the elimination of inessential points by a suitable two-point measure, followed by a direct (exact) solution by quadratic programming, outperforms iterative methods that compute an approximate solution by solving the dual problem.
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01863587
Contributor : Luc Pronzato <>
Submitted on : Tuesday, August 28, 2018 - 5:20:58 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:35 PM
Document(s) archivé(s) le : Thursday, November 29, 2018 - 5:45:48 PM

File

Miniball_OMS-REV1.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Luc Pronzato. On the elimination of inessential points in the smallest enclosing ball problem. Optimization Methods and Software, Taylor & Francis, 2019, 34 (2), pp.225-247. ⟨10.1080/10556788.2017.1359266⟩. ⟨hal-01863587⟩

Share

Metrics

Record views

419

Files downloads

115