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

Hong T. M. Chu (), Ling Liang (), Kim-Chuan Toh () and Lei Yang ()
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Hong T. M. Chu: National University of Singapore
Ling Liang: National University of Singapore
Kim-Chuan Toh: National University of Singapore
Lei Yang: Sun Yat-Sen University

Computational Optimization and Applications, 2023, vol. 85, issue 1, No 4, 107-146

Abstract: 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.

Keywords: Linear programming; Proximal point algorithm; Entropic proximal term; Block coordinate descent; Capacity constrained multi-marginal optimal transport (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-023-00459-2

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