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 eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Mathematics, 1955
• Subjects: Mathematics.; Operations research.; Decision making.; Applied mathematics.; Engineering mathematics.; Calculus of variations.; Management science.; Engineering economics.; Engineering economy.; Calculus of Variations and Optimal Control; Optimization.; Operations Research, Management Science.; Engineering Economics, Organization, Logistics, Marketing.; Operation Research/Decision Theory.; Applications of Mathematics.

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:

• Introduction: The Models
• The Mathematical Models
• Traffic Plans
• The Structure of Optimal Traffic Plans
• Operations on Traffic Plans
• Traffic Plans and Distances between Measures
• The Tree Structure of Optimal Traffic Plans and their Approximation
• Interior and Boundary Regularity
• The Equivalence of Various Models
• Irrigability and Dimension
• The Landscape of an Optimal Pattern
• The Gilbert-Steiner Problem
• Dirac to Lebesgue Segment: A Case Study
• Application: Embedded Irrigation Networks
• Open Problems.