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A regularized interior point method for sparse optimal transport on graphs

Author

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  • Cipolla, S.
  • Gondzio, J.
  • Zanetti, F.

Abstract

In this work, the authors address the Optimal Transport (OT) problem on graphs using a proximal stabilized Interior Point Method (IPM). In particular, strongly leveraging on the induced primal–dual regularization, the authors propose to solve large scale OT problems on sparse graphs using a bespoke IPM algorithm able to suitably exploit primal–dual regularization in order to enforce scalability. Indeed, the authors prove that the introduction of the regularization allows to use sparsified versions of the normal Newton equations to inexpensively generate IPM search directions. A detailed theoretical analysis is carried out showing the polynomial convergence of the inner algorithm in the proposed computational framework. Moreover, the presented numerical results showcase the efficiency and robustness of the proposed approach when compared to network simplex solvers.

Suggested Citation

  • Cipolla, S. & Gondzio, J. & Zanetti, F., 2024. "A regularized interior point method for sparse optimal transport on graphs," European Journal of Operational Research, Elsevier, vol. 319(2), pages 413-426.
    • Handle: RePEc:eee:ejores:v:319:y:2024:i:2:p:413-426
    DOI: 10.1016/j.ejor.2023.11.027
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    References listed on IDEAS

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    1. Li, Cong & Wang, Wenjing & Li, Jingya & Xu, Jiatuo & Li, Xiang, 2019. "Community detector on symptom networks with applications to fatty liver disease," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 527(C).
    2. Stefano Cipolla & Jacek Gondzio, 2023. "Proximal Stabilized Interior Point Methods and Low-Frequency-Update Preconditioning Techniques," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1061-1103, June.
    3. Filippo Zanetti & Jacek Gondzio, 2023. "An Interior Point–Inspired Algorithm for Linear Programs Arising in Discrete Optimal Transport," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1061-1078, September.
    4. S. Bellavia, 1998. "Inexact Interior-Point Method," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 109-121, January.
    5. Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
    6. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    7. Castro, Jordi & Nasini, Stefano, 2021. "A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks," European Journal of Operational Research, Elsevier, vol. 290(3), pages 857-869.
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