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

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 efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with easy-to-implement dual block coordinate descent method subsolver. Unlike existing entropy-type algorithms, our iEPPA employs more practically checkable stopping condition solving the associated subproblems while achieving provable convergence. Moreover, when capacity constrained multi-marginal transport (CMOT) problem (a special case problem), is able to bypass underlying numerical instability issues that often appear popular regularization approach, since does not require parameter be very small order obtain accurate approximate solution. Numerous experiments show efficient robust some CMOT on synthetic data. The preliminary tomography also highlight potential model.