Second‐order cone programming models for the unitary weighted Weber problem and for the minimum sum of the squares clustering problem

Author:

Linhares Marcella Braga de Assis1ORCID,Pinto Renan Vicente2,Maculan Nelson1,Negreiros Marcos3

Affiliation:

1. PESC/COPPE Federal University of Rio de Janeiro Rio de Janeiro Brazil

2. Department of Mathematics Federal Rural University of Rio de Janeiro, Seropedica Rio de Janeiro Brazil

3. Scientific Computing Laboratory, State University of Ceará Fortaleza Ceará Brazil

Abstract

AbstractIn this work, new mixed integer nonlinear optimization models are proposed for two clustering problems: the unitary weighted Weber problem and the minimum sum of squares clustering. The proposed formulations are convex quadratic models with linear and second‐order cone constraints that can be efficiently solved by interior point algorithms. Their continuous relaxation is convex and differentiable. The numerical experiments show the proposed models are more efficient than some classical models for these problems known in the literature.

Publisher

Wiley

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