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  4. GRAPH-STRUCTURED TENSOR OPTIMIZATION FOR NONLINEAR DENSITY CONTROL AND MEAN FIELD GAMES
 
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research article

GRAPH-STRUCTURED TENSOR OPTIMIZATION FOR NONLINEAR DENSITY CONTROL AND MEAN FIELD GAMES

Ringh, Axel
•
Haasler, Isabel  
•
Chen, Yongxin
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2024
SIAM Journal on Control and Optimization

In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problem. This type of problem, which can be seen as a generalization of multimarginal optimal transport problems with graph-structured costs, appears in many applications. Examples are unbalanced optimal transport and multispecies potential mean field games, where the latter is a class of nonlinear density control problems. The method we develop is based on coordinate ascent in a Lagrangian dual, and under mild assumptions we prove that the algorithm converges globally. Moreover, under a set of stricter assumptions, the algorithm converges R-linearly. To perform the coordinate ascent steps one has to compute projections of the tensor, and doing so by brute force is in general not computationally feasible. Nevertheless, for certain graph structures it is possible to derive efficient methods for computing these projections, and here we specifically consider the graph structure that occurs in multispecies potential mean field games. We also illustrate the methodology on a numerical example from this problem class.

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Type
research article
DOI
10.1137/23M1571587
Scopus ID

2-s2.0-85200988206

Author(s)
Ringh, Axel
•
Haasler, Isabel  
•
Chen, Yongxin
•
Karlsson, Johan
Date Issued

2024

Published in
SIAM Journal on Control and Optimization
Volume

62

Issue

4

Start page

2176

End page

2202

Subjects

large-scale convex optimization

•

optimal transport

•

potential mean field games

•

Sinkhorn algorithm

•

tensor optimization

•

unbalanced optimal transport

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LTS4  
FunderFunding(s)Grant NumberGrant URL

KTH Digital Futures

NSF

1942523,2206576

Knut and Alice Wallenberg Foundation

KAW 2018.0349,KAW 2021.0274

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Available on Infoscience
January 24, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/243584
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