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

The discrete optimal transport (OT) problem, which offers an effective computational tool for comparing two discrete probability distributions, has recently attracted much attention and played essential roles in many modern applications. This paper proposes to solve the discrete OT problem by applying a squared smoothing Newton method via the Huber smoothing function for solving the corresponding KKT system directly. The proposed algorithm admits appealing convergence properties and is able to take advantage of the solution sparsity to greatly reduce computational costs. Moreover, the algorithm can be extended to solve problems with similar structures, including the Wasserstein barycenter (WB) problem with fixed supports. To verify the practical performance of the proposed method, we conduct extensive numerical experiments to solve a large set of discrete OT and WB benchmark problems. Our numerical results show that the proposed method is efficient compared to state-of-the-art linear programming (LP) solvers. Moreover, the proposed method consumes less memory than existing LP solvers, which demonstrates the potential usage of our algorithm for solving large-scale OT and WB problems.

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

Cited by 2 publications

References 32 publications

A Corrected Inexact Proximal Augmented Lagrangian Method with a Relative Error Criterion for a Class of Group-Quadratic Regularized Optimal Transport Problems

A Corrected Inexact Proximal Augmented Lagrangian Method with a Relative Error Criterion for a Class of Group-Quadratic Regularized Optimal Transport Problems

A Sparse Smoothing Newton Method for Solving Discrete Optimal Transport Problems

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