Numerical Methods For Viscosity Solutions And Applications
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Numerical Methods For Viscosity Solutions And Applications
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Author : Maurizio Falcone
language : en
Publisher: World Scientific
Release Date : 2001
Numerical Methods For Viscosity Solutions And Applications written by Maurizio Falcone and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications
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Author : Yves Achdou
language : en
Publisher: Springer
Release Date : 2013-05-24
Hamilton Jacobi Equations Approximations Numerical Analysis And Applications written by Yves Achdou and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-24 with Mathematics categories.
These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Optimal Control And Viscosity Solutions Of Hamilton Jacobi Bellman Equations
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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Optimal Control And Viscosity Solutions Of Hamilton Jacobi Bellman Equations written by Martino Bardi 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 2009-05-21 with Science categories.
The purpose of the present book is to offer an up-to-date account of the theory of viscosity solutions of first order partial differential equations of Hamilton-Jacobi type and its applications to optimal deterministic control and differential games. The theory of viscosity solutions, initiated in the early 80's by the papers of M.G. Crandall and P.L. Lions [CL81, CL83], M.G. Crandall, L.C. Evans and P.L. Lions [CEL84] and P.L. Lions' influential monograph [L82], provides an - tremely convenient PDE framework for dealing with the lack of smoothness of the value functions arising in dynamic optimization problems. The leading theme of this book is a description of the implementation of the viscosity solutions approach to a number of significant model problems in op- real deterministic control and differential games. We have tried to emphasize the advantages offered by this approach in establishing the well-posedness of the c- responding Hamilton-Jacobi equations and to point out its role (when combined with various techniques from optimal control theory and nonsmooth analysis) in the important issue of feedback synthesis.
Stochastic And Differential Games
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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic And Differential Games written by Martino Bardi 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 2012-12-06 with Mathematics categories.
The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.
Controlled Markov Processes And Viscosity Solutions
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Author : Wendell H. Fleming
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-04
Controlled Markov Processes And Viscosity Solutions written by Wendell H. Fleming 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 2006-02-04 with Mathematics categories.
This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. It covers dynamic programming for deterministic optimal control problems, as well as to the corresponding theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.
Hamilton Jacobi Bellman Equations
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Author : Dante Kalise
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-06
Hamilton Jacobi Bellman Equations written by Dante Kalise 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 2018-08-06 with Mathematics categories.
Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme
Hamilton Jacobi Equations Theory And Applications
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Author : Hung V. Tran
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-16
Hamilton Jacobi Equations Theory And Applications written by Hung V. Tran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-16 with Education categories.
This book gives an extensive survey of many important topics in the theory of Hamilton–Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly, the basic well-posedness theory of viscosity solutions for first-order Hamilton–Jacobi equations is covered. Then, the homogenization theory, a very active research topic since the late 1980s but not covered in any standard textbook, is discussed in depth. Afterwards, dynamical properties of solutions, the Aubry–Mather theory, and weak Kolmogorov–Arnold–Moser (KAM) theory are studied. Both dynamical and PDE approaches are introduced to investigate these theories. Connections between homogenization, dynamical aspects, and the optimal rate of convergence in homogenization theory are given as well. The book is self-contained and is useful for a course or for references. It can also serve as a gentle introductory reference to the homogenization theory.
Mathematics And Computation In Imaging Science And Information Processing
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Author : Say Song Goh
language : en
Publisher: World Scientific
Release Date : 2007
Mathematics And Computation In Imaging Science And Information Processing written by Say Song Goh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computers categories.
The explosion of data arising from rapid advances in communication, sensing and computational power has concentrated research effort on more advanced techniques for the representation, processing, analysis and interpretation of data sets. In view of these exciting developments, the program OC Mathematics and Computation in Imaging Science and Information ProcessingOCO was held at the Institute for Mathematical Sciences, National University of Singapore, from July to December 2003 and in August 2004 to promote and facilitate multidisciplinary research in the area. As part of the program, a series of tutorial lectures were conducted by international experts on a wide variety of topics in mathematical image, signal and information processing. This compiled volume contains survey articles by the tutorial speakers, all specialists in their respective areas. They collectively provide graduate students and researchers new to the field a unique and valuable introduction to a range of important topics at the frontiers of current research. Sample Chapter(s). Foreword (46 KB). Chapter 1: Subdivision on Arbitrary Meshes: Algorithms and Theory (771 KB). Contents: Subdivision on Arbitrary Meshes: Algorithms and Theory (D Zorin); High Order Numerical Methods for Time Dependent Hamilton-Jacobi Equations (C-W Shu); Theory and Computation of Variational Image Deblurring (T F Chan & J Shen); Data Hiding OCo Theory and Algorithms (P Moulin & R Koetter); Image Steganography and Steganalysis: Concepts and Practice (M Kharrazi et al.); The Apriori Algorithm OCo A Tutorial (M Hegland). Readership: Graduate students and researchers in mathematical image, signal and information processing."
Numerical Analysis Of Spectral Methods
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Author : David Gottlieb
language : en
Publisher: SIAM
Release Date : 1977-01-01
Numerical Analysis Of Spectral Methods written by David Gottlieb and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Technology & Engineering categories.
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Interfaces Modeling Analysis Numerics
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Author : Eberhard Bänsch
language : en
Publisher: Springer Nature
Release Date : 2023-10-10
Interfaces Modeling Analysis Numerics written by Eberhard Bänsch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Mathematics categories.
These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization. We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.