Optimal Transportation Networks
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Optimal Transportation Networks
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Author : Marc Bernot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009
Optimal Transportation Networks written by Marc Bernot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Business & Economics categories.
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 whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
Lectures On Optimal Transport
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Author : Luigi Ambrosio
language : en
Publisher: Springer Nature
Release Date : 2024-12-28
Lectures On Optimal Transport written by Luigi Ambrosio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-28 with Mathematics categories.
This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations. This is the second edition of the book, first published in 2018. It includes refinement of proofs, an updated bibliography and a more detailed discussion of minmax principles, with the aim of giving two fully self-contained proofs of Kantorovich duality.
Optimal Transport Methods In Economics
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Author : Alfred Galichon
language : en
Publisher: Princeton University Press
Release Date : 2018-08-14
Optimal Transport Methods In Economics written by Alfred Galichon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-14 with Business & Economics categories.
Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. The first introduction to the subject written especially for economists Includes programming examples Features numerous exercises throughout Ideal for students and researchers alike
Network Design With Applications To Transportation And Logistics
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Author : Teodor Gabriel Crainic
language : en
Publisher: Springer Nature
Release Date : 2021-07-16
Network Design With Applications To Transportation And Logistics written by Teodor Gabriel Crainic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-16 with Business & Economics categories.
This book explores the methodological and application developments of network design in transportation and logistics. It identifies trends, challenges and research perspectives in network design for these areas. Network design is a major class of problems in operations research where network flow, combinatorial and mixed integer optimization meet. The analysis and planning of transportation and logistics systems continues to be one of the most important application areas of operations research. Networks provide the natural way of depicting such systems, so the optimal design and operation of networks is the main methodological area of operations research that is used for the analysis and planning of these systems. This book defines the current state of the art in the general area of network design, and then turns to its applications to transportation and logistics. New research challenges are addressed. Network Design with Applications to Transportation and Logistics is divided into three parts. Part I examines basic design problems including fixed-cost network design and parallel algorithms. After addressing the basics, Part II focuses on more advanced models. Chapters cover topics such as multi-facility network design, flow-constrained network design, and robust network design. Finally Part III is dedicated entirely to the potential application areas for network design. These areas range from rail networks, to city logistics, to energy transport. All of the chapters are written by leading researchers in the field, which should appeal to analysts and planners.
An Algorithm For Synthesizing Optimal Transportation Networks
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Author : Kent Leland Groninger
language : en
Publisher:
Release Date : 1971
An Algorithm For Synthesizing Optimal Transportation Networks written by Kent Leland Groninger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Network analysis (Planning) categories.
Optimal Urban Networks Via Mass Transportation
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Author : Giuseppe Buttazzo
language : en
Publisher: Springer
Release Date : 2008-11-09
Optimal Urban Networks Via Mass Transportation written by Giuseppe Buttazzo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-09 with Mathematics categories.
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where," optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
Optimal Transport For Applied Mathematicians
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Author : Filippo Santambrogio
language : en
Publisher: Birkhäuser
Release Date : 2015-10-17
Optimal Transport For Applied Mathematicians written by Filippo Santambrogio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-17 with Mathematics categories.
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
Urban Transportation Networks
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Author : Yosef Sheffi
language : es
Publisher: Prentice Hall
Release Date : 1984
Urban Transportation Networks written by Yosef Sheffi and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Political Science categories.
An Algorithm For Synthesizing Optimal Transportation Networks
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Author : Kent Leland Groninger
language : en
Publisher:
Release Date : 1971
An Algorithm For Synthesizing Optimal Transportation Networks written by Kent Leland Groninger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Network analysis (Planning) categories.
Modeling Dynamic Transportation Networks
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Author : Bin Ran
language : en
Publisher: Springer
Release Date : 2011-12-10
Modeling Dynamic Transportation Networks written by Bin Ran and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-10 with Business & Economics categories.
This book seeks to summarize our recent progress in dynamic trans portation network modeling. It concentrates on ideal dynamic network models based on actual travel times and their corresponding solution algorithms. In contrast, our first book DynamIc Urban Transportation Network Models - The ory and Implications for Intelligent Vehicle-Hzghway Systems (Springer-Verlag, 1994) focused on instantaneous dynamic network models. Comparing the two books, the major differences can be summarized as follows: 1. This book uses the variational inequality problem as the basic formulation approach and considers the optimal control problem as a subproblem for solution purposes. The former book used optimal control theory as the basic formulation approach, which caused critical problems in some circumstances. 2. This book focuses on ideal dynamic network models based on actual travel times. The former book focused on instantaneous dynamic network models based on currently prevailing travel times. 3. This book formulates a stochastic dynamic route choice model which can utilize any possible route choice distribution function instead of only the logit function. 4. This book reformulates the bilevel problem of combined departure time/ route choice as a one-level variational inequality. 5. Finally, a set of problems is provided for classroom use. In addition, this book offers comprehensive insights into the complexity and challenge of applying these dynamic network models to Intelligent Trans portation Systems (ITS). Nevertheless, the models in this text are not yet fully evaluated and are subject to revision based on future research.