Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 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

Inexact JKO and proximal-gradient algorithms in the Wasserstein space (2505.23517v2)

Published 29 May 2025 in math.OC

Abstract: This paper studies the convergence properties of the inexact Jordan-Kinderlehrer-Otto (JKO) scheme and proximal-gradient algorithm in the context of Wasserstein spaces. The JKO scheme, a widely-used method for approximating solutions to gradient flows in Wasserstein spaces, typically assumes exact solutions to iterative minimization problems. However, practical applications often require approximate solutions due to computational limitations. This work focuses on the convergence of the scheme to minimizers for the underlying functional and addresses these challenges by analyzing two types of inexactness: errors in Wasserstein distance and errors in energy functional evaluations. The paper provides rigorous convergence guarantees under controlled error conditions, demonstrating that weak convergence can still be achieved with inexact steps. The analysis is further extended to proximal-gradient algorithms, showing that convergence is preserved under inexact evaluations.

Summary

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

X Twitter Logo Streamline Icon: https://streamlinehq.com