Abstract

We propose a moment relaxation for two problems, the separation and covering problems with semialgebraic sets generated by a polynomial of degree $d$. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order $r$ increases, and (b) after performing some small perturbation of the original problem, convergence can be achieved with $r=d$. We further provide a practical iterative algorithm that is computationally tractable for large datasets and present encouraging computational results.

Keywords

  1. moment relaxations
  2. semidefinite programming
  3. minimum-volume covering ellipsoid
  4. separation problem

MSC codes

  1. 90C22

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Information & Authors

Information

Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 3127 - 3144
ISSN (online): 1095-7189

History

Submitted: 9 February 2018
Accepted: 21 September 2018
Published online: 13 November 2018

Keywords

  1. moment relaxations
  2. semidefinite programming
  3. minimum-volume covering ellipsoid
  4. separation problem

MSC codes

  1. 90C22

Authors

Affiliations

Funding Information

Agence Nationale de la Recherche https://doi.org/10.13039/501100001665 : ANR-11-LABX-0025-01
H2020 European Research Council https://doi.org/10.13039/100010663 : 666981
H2020 European Research Council https://doi.org/10.13039/100010663 : 306595

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