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

arXiv: https://arxiv.org/abs/2011.14312 · HTML: https://mlsanity.com/paper/2011.14312/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [PINS: Proximal Iterations with Sparse Newton and Sinkhorn for Optimal Transport](https://mlsanity.com/paper/2502.03749/) (2025)
- [On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem](https://mlsanity.com/paper/2507.15264/) (2025)
- [Accelerating Multi-Block Constrained Optimization Through Learning to Optimize](https://mlsanity.com/paper/2409.17320/) (2024)
- [A Provably Convergent and Practical Algorithm for Gromov--Wasserstein Optimal Transport](https://mlsanity.com/paper/2605.04175/) (2026)
- [An inexact Bregman proximal point method and its acceleration version for unbalanced optimal transport](https://mlsanity.com/paper/2402.16978/) (2024)

## Abstract (arXiv)

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 large-scale CMOT problems. The experiments on the discrete tomography problem also highlight the potential modeling power of our model.