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

In 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 effici...

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Bibliographic Details
Published in:International transactions in operational research 2025-03, Vol.32 (2), p.961-972
Main Authors: Linhares, Marcella Braga de Assis, Pinto, Renan Vicente, Maculan, Nelson, Negreiros, Marcos
Format: Article
Language:English
Subjects:
Algorithms
Clustering
clustering problem
combinatorial optimization
Mixed integer
nonlinear programming
Optimization models
second‐order cone programming
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Summary:In 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.
ISSN:0969-6016
1475-3995
DOI:10.1111/itor.13472