Hong T. M. Chu, Department of Mathematics, National University of Singapore (hongtmchu@u.nus.edu).

Ling Liang, Department of Mathematics, National University of Singapore (liang.ling@u.nus.edu).

Kim-Chuan Toh, Department of Mathematics, and Institute of Operations Research and Analytics, National University of Singapore
(mattohkc@nus.edu.sg).

Lei Yang, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China. (yanglei.math@gmail.com).

 

This research is supported by the Ministry of Education, Singapore, under its 2019 Academic Research Fund Tier 3 grant call (Award ref: MOE-2019-T3-1-010)
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.