Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
134 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

An Efficient Augmented Lagrangian Method for Dynamic Optimal Transport on Surfaces Based on Second-Order Cone Programming (2506.08988v1)

Published 10 Jun 2025 in math.OC

Abstract: This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path. Building on the convex DOT model of Benamou and Brenier, we first properly reformulate its dual problem, discretized on a triangular mesh for space together with a staggered grid for time, to a linear second-order cone programming. Then the resulting finite-dimensional convex optimization problem is solved via an inexact semi-proximal augmented Lagrangian method with a highly efficient numerical implementation, and the algorithm is guaranteed to converge to a Karush-Kuhn-Tucker solution without imposing any additional assumptions. Finally, we implement the proposed methodology as an open-source software package. The effectiveness, robustness, and computational efficiency of the software are demonstrated through extensive numerical experiments across diverse datasets, where it consistently outperforms state-of-the-art solvers by several times in speed.

Summary

We haven't generated a summary for this paper yet.