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: 5751 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: This book offers an in-depth overview of polyhedral methods and efficient algorithms in combinatorial optimization.These methods form a broad, coherent and powerful kernel in combinatorial optimization, with strong links to discrete mathematics, mathematical programming and computer science. In eight parts, various areas are treated, each starting with an elementary introduction to the area, with short, elegant proofs of the principal results, and each evolving to the more advanced methods and results, with full proofs of some of the deepest theorems in the area. Over 4000 references to further research are given, and historical surveys on the basic subjects are presented.
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: Weintraub, Steven Название: Differential forms ISBN: 0123944031 ISBN-13(EAN): 9780123944030 Издательство: Elsevier Science Рейтинг: Цена: 9504 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Differential forms are a powerful mathematical technique to help students, researchers, and engineers solve problems in geometry and analysis, and their applications. They both unify and simplify results in concrete settings, and allow them to be clearly and effectively generalized to more abstract settings. Differential Forms has gained high recognition in the mathematical and scientific community as a powerful computational tool in solving research problems and simplifying very abstract problems. Differential Forms, 2nd Edition, is a solid resource for students and professionals needing a general understanding of the mathematical theory and to be able to apply that theory into practice.
Автор: Terry L. Friesz Название: Dynamic Optimization and Differential Games ISBN: 0387727779 ISBN-13(EAN): 9780387727776 Издательство: Springer Рейтинг: Цена: 24976 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.
Автор: Sundaram, Rangarajan K. Название: A First Course in Optimization Theory ISBN: 0521497701 ISBN-13(EAN): 9780521497701 Издательство: Cambridge Academ Рейтинг: Цена: 4140 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book introduces students to optimization theory and its use in economics and allied disciplines.
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: Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions.
Описание: This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Описание: This book fills a gap between theory-oriented investigations in PDE-constrained optimization and the practical demands made by numerical solutions of PDE optimization problems. The authors discuss computational techniques representing recent developments that result from a combination of modern techniques for the numerical solution of PDEs and for sophisticated optimization schemes. Computational Optimization of Systems offers readers a combined treatment of PDE-constrained optimization and uncertainties and an extensive discussion of multigrid optimization. It provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization. It will also help researchers in the natural sciences and engineering to formulate and solve optimization problems.
Описание: Differential-algebraic equations (DAEs) are the most natural way to mathematically model many complex systems in science and engineering. This book provides a guide to the theory and practice of modelling with DAEs. In particular, the reader will learn to maximise the performance of their models by optimising the design parameters. Presented within are cutting-edge theory and state-of-the-art numerical methods for the optimal control of differential-algebraic equations, alongside real-world applications of the results. This accessible treatment of the subject, written by leading experts, is suitable for applied mathematicians, engineers and computational scientists from a variety of disciplines. It will be of interest to those developing theory and those working on real-world applications, especially in the optimal control of problems in chemical and mechanical engineering.
Описание: This book aims to address the coordination of quality control with other aspects of a firm's production system and supply chain, specifically, the coordination between the inspection-repair of finished products and their follow-up services, between inspection and process revision, between production and inspection under capacity constraints, between replenishment and rework quantities, and between supply and substitution decisions. To address these issues, the authors have in recent years developed a set of dynamic approaches based on Markov decision programming and using stochastic comparison techniques, including those based on notions of stochastic convexity and submodularity. The focal question driving their studies is this: under what conditions and for what systems does a certain class of policies become optimal in the sense of striking the best coordination among several competing or even conflicting aspects in the production-inventory system? Particular emphasis has been put on the class of policies that have simple, threshold structures -- simple enough to facilitate implementation, but sophisticated enough to be optimal. Written in a self-contained and well-motivated manner, the book offers a timely and useful text or reference to researchers and practitioners in operations research and management, industrial and quality engineering, systems and control, applied mathematics and statistics, and related fields.
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