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Mathematics > Optimization and Control

arXiv:2210.16456 (math)
[Submitted on 29 Oct 2022]

Title:Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions

Authors:Jason M. Altschuler
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Abstract:In this short expository note, we describe a unified algorithmic perspective on several classical problems which have traditionally been studied in different communities. This perspective views the main characters -- the problems of Optimal Transport, Minimum Mean Cycle, Matrix Scaling, and Matrix Balancing -- through the same lens of optimization problems over joint probability distributions P(x,y) with constrained marginals. While this is how Optimal Transport is typically introduced, this lens is markedly less conventional for the other three problems. This perspective leads to a simple and unified framework spanning problem formulation, algorithm development, and runtime analysis.
Comments: Invited expository article for the SIAM Group on Optimization's Views and News
Subjects: Optimization and Control (math.OC); Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2210.16456 [math.OC]
  (or arXiv:2210.16456v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.16456

Submission history

From: Jason Altschuler [view email]
[v1] Sat, 29 Oct 2022 01:04:19 UTC (65 KB)
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