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An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems

Author

Listed:
  • Hong T. M. Chu

    (National University of Singapore)

  • Ling Liang

    (National University of Singapore)

  • Kim-Chuan Toh

    (National University of Singapore
    National University of Singapore)

  • Lei Yang

    (Sun Yat-Sen University)

Abstract

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving some large-scale CMOT problems on synthetic data. The preliminary experiments on the discrete tomography problem also highlight the potential modeling capability of our model.

Suggested Citation

  • Hong T. M. Chu & Ling Liang & Kim-Chuan Toh & Lei Yang, 2023. "An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems," Computational Optimization and Applications, Springer, vol. 85(1), pages 107-146, May.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:1:d:10.1007_s10589-023-00459-2
    DOI: 10.1007/s10589-023-00459-2
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    References listed on IDEAS

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