LQ Dynamic Optimization and Differential Games, Jacob Engwerda
Автор: Strang Название: Differential Equations and Linear Algebra ISBN: 0980232791 ISBN-13(EAN): 9780980232790 Издательство: Cambridge Academ Рейтинг: Цена: 5203 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Описание: A text for a graduate level course in the theory of ordinary differential equations. It contains theory and applications. It links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and abstract algebra.
Автор: Van der Put Marius , Singer Michael F. Название: Galois Theory of Linear Differential Equations ISBN: 3540442286 ISBN-13(EAN): 9783540442288 Издательство: Springer Рейтинг: Цена: 9345 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.
Описание: Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and
algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a
wide variety of fields. "LQ Dynamic Optimization and Differential Games" is an assessment of the state of the art in its field and the first modern book on linear quadratic game theory,
one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management.
Linear quadratic dynamic models have a
long tradition in economics, operations research and control engineering; and the author begins by describing the one decision maker LQ dynamic optimization problem before
introducing LQ differential games. It covers cooperative and non cooperative scenarios, and treats the standard information structures (open loop and feedback). It includes real life
economic examples to illustrate theoretical concepts and results.
It presents problem formulations and sound mathematical problem analysis. It includes exercises and
solutions, enabling use for self study or as a course text. It is supported by a website featuring solutions to exercises, further examples and computer code for numerical
"LQ Dynamic Optimization and Differential Games" offers a comprehensive introduction to the theory and practice of this extensively used class of economic
models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering
and management science.
Описание: Evolutionary Algorithms (EAs) have grown into a mature field of research in optimization, and have proven to be effective and robust problem solvers for a broad range of static real-world optimization problems. Yet, since they are based on the principles of natural evolution, and since natural evolution is a dynamic process in a changing environment, EAs are also well suited to dynamic optimization problems. Evolutionary Optimization in Dynamic Environments is the first comprehensive work on the application of EAs to dynamic optimization problems. It provides an extensive survey on research in the area and shows how EAs can be successfully used to continuously and efficiently adapt a solution to a changing environment, find a good trade-off between solution quality and adaptation cost, find robust solutions whose quality is insensitive to changes in the environment, find flexible solutions which are not only good but that can be easily adapted when necessary. All four aspects are treated in this book, providing a holistic view on the challenges and opportunities when applying EAs to dynamic optimization problems. The comprehensive and up-to-date coverage of the subject, together with details of latest original research, makes Evolutionary Optimization in Dynamic Environments an invaluable resource for researchers and professionals who are dealing with dynamic and stochastic optimization problems, and who are interested in applying local search heuristics, such as evolutionary algorithms.
Описание: This book is concerned with the analysis, optimization and controllability of time-discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non-cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications.
Автор: Yeung David W.K., Petrosyan Leon A. Название: Cooperative Stochastic Differential Games ISBN: 0387276203 ISBN-13(EAN): 9780387276205 Издательство: Springer Рейтинг: Цена: 13089 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Stochastic differential games represent one of the most complex forms of decision making under uncertainty. In particular, interactions between strategic behaviors, dynamic evolution and stochastic elements have to be considered simultaneously. The complexity of stochastic differential games generally leads to great difficulties in the derivation of solutions. Cooperative games hold out the promise of more socially optimal and group efficient solutions to problems involving strategic actions. Despite urgent calls for national and international cooperation, the absence of formal solutions has precluded rigorous analysis of this problem.
Автор: Yong Jiongmin Название: Differential Games ISBN: 9814596221 ISBN-13(EAN): 9789814596220 Издательство: World Scientific Publishing Рейтинг: Цена: 11536 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This Book Uses A Small Volume To Present The Most Basic Results For Deterministic Two-Person Differential Games. The Presentation Begins With Optimization Of A Single Function, Followed By A Basic Theory For Two-Person Games. For Dynamic Situations, The Author First Recalls Control Theory Which Is Treated As Single-Person Differential Games. Then A Systematic Theory Of Two-Person Differential Games Is Concisely Presented, Including Evasion And Pursuit Problems, Zero-Sum Problems And Lq Differential Games.The Book Is Intended To Be Self-Contained, Assuming That The Readers Have Basic Knowledge Of Calculus, Linear Algebra, And Elementary Ordinary Differential Equations. The Readership Of The Book Could Be Junior/Senior Undergraduate And Graduate Students With Majors Related To Applied Mathematics, Who Are Interested In Differential Games. Researchers In Some Other Related Areas, Such As Engineering, Social Science, Etc. Will Also Find The Book Useful.
Описание: The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games.This is the first title in SIAM’s Financial Mathematics book series and is based on the author’s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean-Vlasov dynamics.The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
Описание: This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
Описание: Includes the proof of the fundamental Doob-Meyer decomposition theorem. This book contains the more general version of the Girsanov theorem due to Lenglart and martingale representation, including both the Jacod-Yor theory and Emery`s examples of martingales that actually have martingale representation.
Автор: Terry L. Friesz Название: Dynamic Optimization and Differential Games ISBN: 0387727779 ISBN-13(EAN): 9780387727776 Издательство: Springer Рейтинг: Цена: 22347 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Addresses the increasing number of Operations Research and Management Science problems (that is, applications) that involve the explicit consideration of time and of gaming among multiple agents. This book is suitable for engineers, operation researchers, applied mathematicians and social scientists.
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