Optimal Transportation Networks Models and Theory /

• Main Authors: Bernot, Marc. (Author), Caselles, Vicent. (Author), Morel, Jean-Michel. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1955
• Subjects: Mathematics.; Mathematical optimization.; Operations research.; Engineering economy.; Calculus of Variations and Optimal Control; Optimization.; Operations Research, Mathematical Programming.; Engineering Economics, Organization, Logistics, Marketing.; Operations Research/Decision Theory.; Applications of Mathematics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-69315-4

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional...

Table of Contents:

• 1 Introduction: the models
• 2 The mathematical models
• 3 Traffic plans
• 4 The structure of optimal traffic plans
• 5 Operations on traffic plans
• 6 Traffic plans and distances between measures
• 7 The tree structure of optimal traffic plans and their approximation
• 8 Interior and boundary regularity
• 9 The equivalence of various models
• 10 Irrigability and dimension
• 11 The landscape of an optimal pattern
• 12 The Gilbert-Steiner problem
• 13 Dirac to Lebesgue segment: a case study
• 14 Application: embedded irrigation networks
• 15 Open problems
• A Skorokhod Theorem
• B Flows in tubes
• C Notations.