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Stability of optimal traffic plans in the irrigation problem

Authors :
Antoine Prouff
Antonio De Rosa
Andrea Marchese
Maria Colombo
Paul Pegon
Ecole Polytechnique Fédérale de Lausanne (EPFL)
Courant Institute of Mathematical Sciences [New York] (CIMS)
New York University [New York] (NYU)
NYU System (NYU)-NYU System (NYU)
Department of mathematics/Dipartimento di Matematica [Univ. Trento]
Università degli Studi di Trento (UNITN)
CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN)
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay)
Maria Colombo was partially supported by the Swiss National Science Foundation grant 200021_182565. Antonio De Rosa has been supported by the NSF DMS Grant No. 1906451. Andrea Marchese acknowledges partial support from GNAMPA-INdAM.
Department of Mathematics [College Park]
University of Maryland [College Park]
University of Maryland System-University of Maryland System
Bocconi Institute for Data Science and Analytics (BIDSA)
Bocconi University [Milan, Italy]
Université Paris Dauphine-PSL
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris
M. C. was partially supported by the Swiss National Science Foundation grant 200021_182565. A. D. R. has been supported by the NSF DMS Grant No. 1906451 and the NSF DMS Grant No. 2112311. A. M. acknowledges partial support from GNAMPA-INdAM. A.P. was supported by the Fondation Mathématiques Jacques Hadamard. P.P and A.P. both acknowledge EPFL for hosting them during the semester this paper was prepared.
Inria de Paris
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
Source :
Discrete and Continuous Dynamical Systems-Series A, Discrete and Continuous Dynamical Systems-Series A, In press, ⟨10.3934/dcds.2021167⟩
Publication Year :
2022

Abstract

We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [7], extending it to the Lagrangian framework.

Subjects

Subjects :
BRANCHED TRANSPORT
Mathematical optimization
Irrigation
TRAFFIC PLANS
[MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA]
01 natural sciences
Stability (probability)
symbols.namesake
Mathematics - Analysis of PDEs
Classical Analysis and ODEs (math.CA)
FOS: Mathematics
Computer Science::Networking and Internet Architecture
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Discrete Mathematics and Combinatorics
Limit (mathematics)
0101 mathematics
Mathematics - Optimization and Control
Mathematics
TRANSPORTATION NETWORK, BRANCHED TRANSPORT, IRRIGATION PROBLEM, TRAFFIC PLANS, STABILITY
STABILITY
IRRIGATION PROBLEM
Applied Mathematics
TRANSPORTATION NETWORK
010102 general mathematics
Eulerian path
Flow network
010101 applied mathematics
Optimization and Control (math.OC)
Mathematics - Classical Analysis and ODEs
symbols
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Analysis
Lagrangian
Analysis of PDEs (math.AP)

Details

Language :
English
ISSN :
10780947
Database :
OpenAIRE
Journal :
Discrete and Continuous Dynamical Systems-Series A, Discrete and Continuous Dynamical Systems-Series A, In press, ⟨10.3934/dcds.2021167⟩
Accession number :
edsair.doi.dedup.....376d60dfb037e21b430167cde1be492b

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