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Optimal Transport For Applied Mathematicians

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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.

Optimal Transport For Applied Mathematicians

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Author : Filippo Santambrogio
language : en
Publisher:
Release Date : 2015

Optimal Transport For Applied Mathematicians written by Filippo Santambrogio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

Topological Optimization And Optimal Transport

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Author : Maïtine Bergounioux
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-08-07

Topological Optimization And Optimal Transport written by Maïtine Bergounioux and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.

By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. Contents Part I Geometric issues in PDE problems related to the infinity Laplace operator Solution of free boundary problems in the presence of geometric uncertainties Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies High-order topological expansions for Helmholtz problems in 2D On a new phase field model for the approximation of interfacial energies of multiphase systems Optimization of eigenvalues and eigenmodes by using the adjoint method Discrete varifolds and surface approximation Part II Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem Optimal transportation theory with repulsive costs Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations On the Lagrangian branched transport model and the equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless Euler equations with maximal density constraint: a time-splitting scheme Convergence of a fully discrete variational scheme for a thin-film equatio Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance

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.

Conversations On Optimal Transport

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Author : Luigi Ambrosio
language : en
Publisher: Springer Nature
Release Date : 2024-05-23

Conversations 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 2024-05-23 with Mathematics categories.

This work is closely tied to the renowned mathematics textbook series known as UNITEXT, tailored for university students pursuing bachelor’s or master’s degrees. What sets this particular book apart in the Springer collection is its unique origin: it has been crafted through a meticulous process involving interviews handled with and by world-class mathematicians. The content featured in this book revolve around a highly relevant and engaging topic: Optimal Transport. These conversations involve not only authors from the UNITEXT series, but also members of the series’ Editorial Board. Additionally, they feature prominent figures in the field, including a Field Medalist. This work provides readers with a snapshot of remarkable vitality and freshness, guaranteed to captivate and engage anyone with an interest in mathematics. It’s important to note that these interviews were initially shared as podcasts and originally broadcasted as online events on the Cassyni platform. Subsequently, advanced AI tools were employed under human supervision to transcribe the audios and edit them for better readability. A human copy-editor was involved during the whole process, and the authors revised the final copy-edited texts before publication. The content in each format – the interviews, the PODCASTS and the book – is self-contained and not a mere adaptation from one medium to another. Instead, it represents an independent exploration of the subject matter.

Optimal Transport And Applications To Geometric Optics

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Author : Cristian E. Gutiérrez
language : en
Publisher: Springer Nature
Release Date : 2023-12-09

Optimal Transport And Applications To Geometric Optics written by Cristian E. Gutiérrez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-09 with Mathematics categories.

This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A chapter on Monge-Ampère measures is included containing also exercises. A detailed analysis of the Wasserstein metric is also carried out. For the applications to optics, the book describes the necessary background concerning light refraction, solving both far-field and near-field refraction problems, and indicates lines of current research in this area. Researchers in the fields of mathematical analysis, optimal transport, partial differential equations (PDEs), optimization, and optics will find this book valuable. It is also suitable for graduate students studying mathematics, physics, and engineering. The prerequisites for this book include a solid understanding of measure theory and integration, as well as basic knowledge of functional analysis.

Optimal Transport

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Author : Gershon Wolansky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-01-18

Optimal Transport written by Gershon Wolansky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.

This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning.

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

Handbook Of Mathematical Models And Algorithms In Computer Vision And Imaging

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Author : Ke Chen
language : en
Publisher: Springer Nature
Release Date : 2023-02-24

Handbook Of Mathematical Models And Algorithms In Computer Vision And Imaging written by Ke Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-24 with Mathematics categories.

This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

Mathematical And Statistical Methods For Actuarial Sciences And Finance

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Author : Marco Corazza
language : en
Publisher: Springer Nature
Release Date : 2024-08-01

Mathematical And Statistical Methods For Actuarial Sciences And Finance written by Marco Corazza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-01 with Mathematics categories.

The book presents a collection of peer-reviewed short papers selected from those presented at the International Conference Mathematical and Statistical Methods for Actuarial Sciences and Finance – MAF2024. The year 2024 marks the twentieth anniversary of the first edition of this conference. The idea behind this book is that collaboration and cross-pollination between mathematicians and statisticians working in actuarial sciences and finance could enhance research in these fields. The effectiveness of this concept has been demonstrated by widespread participation across all editions, held at various locations including the University of Salerno, Italy (2004, 2006, 2010, 2014, and 2022); Ca' Foscari University of Venice, Italy (2008, 2012, and 2020); University Paris-Dauphine in Paris, France (2016); University Carlos III of Madrid, Madrid (2018); and University of Le Havre Normandie, Le Havre, France (2024). This effectiveness is also evident in the attention consistently shown by both the scientific community and professionals toward the volumes of peer-reviewed papers accompanying all past editions of MAF. The book is a valuable resource for academics, researchers, Ph.D. students, and professionals. Furthermore, it is also of interest to other readers with a quantitative background.

Optimal Transport For Applied Mathematicians

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