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We introduce a class of specially structured linear programming (LP)problems, which has favorable modeling capability for important applicationproblems in different areas such as optimal transport, discrete tomography andeconomics. To solve these generally large-scale LP problems efficiently, wedesign an implementable inexact entropic proximal point algorithm (iEPPA)combined with an easy-to-implement dual block coordinate descent method as asubsolver. Unlike existing entropy-type proximal point algorithms, our iEPPAemploys a more practically checkable stopping condition for solving theassociated subproblems while achieving provable convergence. Moreover, whensolving the capacity constrained multi-marginal optimal transport (CMOT)problem (a special case of our LP problem), our iEPPA is able to bypass theunderlying numerical instability issues that often appear in the popularentropic regularization approach, since our algorithm does not require theproximal parameter to be very small in order to obtain an accurate approximatesolution. Numerous numerical experiments show that our iEPPA is efficient androbust for solving large-scale CMOT problems. The experiments on the discretetomography problem also highlight the potential modeling power of our model.

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