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| dynamic optimization book: Dynamic Optimization Morton I. Kamien, Nancy Lou Schwartz, 2012-11-21 An excellent financial research tool, this celebrated classic focuses on the methods of solving continuous time problems. The two-part treatment covers the calculus of variations and optimal control. In the decades since its initial publication, this text has defined dynamic optimization courses taught to economics and management science students. 1998 edition-- |
| dynamic optimization book: Dynamic Optimization Karl Hinderer, Ulrich Rieder, Michael Stieglitz, 2017-01-12 This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained. |
| dynamic optimization book: Elements of Dynamic Optimization Alpha C. Chiang, 1992 An in-depth exploration of dynamic optimization in Economics, written by the author of the best-selling FUNDAMENTAL METHODS OF MATHEMATICAL ECONOMICS. It can be used in sequence with FUNDAMENTAL METHODS, or independently, at the advanced undergraduate or a beginning graduate level. It is written at the same analytical level, with the same care, as the other Chiang text. |
| dynamic optimization book: Principles of Dynamic Optimization Piernicola Bettiol, Richard B. Vinter, 2024-02-16 This monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth treatment of necessary conditions, minimizer regularity, and global optimality conditions related to the Hamilton-Jacobi equation is given. New, streamlined proofs of fundamental theorems are incorporated throughout the text that eliminate earlier, cumbersome reductions and constructions. The first chapter offers an extended overview of dynamic optimization and its history that details the shortcomings of the elementary theory and demonstrates how a deeper analysis aims to overcome them. Aspects of dynamic programming well-matched to analytical techniques are considered in the final chapter, including characterization of extended-value functions associated with problems having endpoint and state constraints, inverse verification theorems, sensitivity relationships, and links to the maximum principle. This text will be a valuable resource for those seeking an understanding of dynamic optimization. The lucid exposition, insights into the field, and comprehensive coverage will benefit postgraduates, researchers, and professionals in system science, control engineering, optimization, and applied mathematics. |
| dynamic optimization book: Optimal Control Theory and Static Optimization in Economics Daniel Léonard, Ngo van Long, 1992-01-31 Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purpose of the book is to draw the parallel between optimal control theory and static optimization. Chapter 1 provides an extensive treatment of constrained and unconstrained maximization, with emphasis on economic insight and applications. Starting from basic concepts, it derives and explains important results, including the envelope theorem and the method of comparative statics. This chapter may be used for a course in static optimization. The book is largely self-contained. No previous knowledge of differential equations is required. |
| dynamic optimization book: Dynamic Optimization for Beginners Piermarco Cannarsa, Filippo Gazzola, 2021 |
| dynamic optimization book: Elements of Dynamic Optimization Alpha C. Chiang, 1992 Designed to be used with Chiang's Fundamental Methods of Mathematical Economics, or independently at advanced undergraduate or graduate level, this text presents an in-depth exploration of dynamic optimization in economics. |
| dynamic optimization book: Dynamic Economics Gregory C. Chow, 1997 This work presents the optimization framework for dynamic economics and treats a number of topics in economics, including growth, macroeconomics, microeconomics, finance and dynamic games. The book also teaches by examples, using concepts to solve simple problems, moving on to general propositions. |
| dynamic optimization book: Dynamic Optimization Arthur Earl Bryson, 1999 Dynamic Optimization takes an applied approach to its subject, offering many examples and solved problems that draw from aerospace, robotics, and mechanics. The abundance of thoroughly tested general algorithms and MATLAB codes provide the reader with the practice necessary to master the subject, while the realistic engineering problems and examples keep the material interesting and relevant. |
| dynamic optimization book: Metaheuristics for Dynamic Optimization Enrique Alba, Amir Nakib, Patrick Siarry, 2014-09-20 This book is an updated effort in summarizing the trending topics and new hot research lines in solving dynamic problems using metaheuristics. An analysis of the present state in solving complex problems quickly draws a clear picture: problems that change in time, having noise and uncertainties in their definition are becoming very important. The tools to face these problems are still to be built, since existing techniques are either slow or inefficient in tracking the many global optima that those problems are presenting to the solver technique. Thus, this book is devoted to include several of the most important advances in solving dynamic problems. Metaheuristics are the more popular tools to this end, and then we can find in the book how to best use genetic algorithms, particle swarm, ant colonies, immune systems, variable neighborhood search, and many other bioinspired techniques. Also, neural network solutions are considered in this book. Both, theory and practice have been addressed in the chapters of the book. Mathematical background and methodological tools in solving this new class of problems and applications are included. From the applications point of view, not just academic benchmarks are dealt with, but also real world applications in logistics and bioinformatics are discussed here. The book then covers theory and practice, as well as discrete versus continuous dynamic optimization, in the aim of creating a fresh and comprehensive volume. This book is targeted to either beginners and experienced practitioners in dynamic optimization, since we took care of devising the chapters in a way that a wide audience could profit from its contents. We hope to offer a single source for up-to-date information in dynamic optimization, an inspiring and attractive new research domain that appeared in these last years and is here to stay. |
| dynamic optimization book: Dynamic Economics Jerome Adda, Russell W. Cooper, 2003-08-29 An integrated approach to the empirical application of dynamic optimization programming models, for students and researchers. This book is an effective, concise text for students and researchers that combines the tools of dynamic programming with numerical techniques and simulation-based econometric methods. Doing so, it bridges the traditional gap between theoretical and empirical research and offers an integrated framework for studying applied problems in macroeconomics and microeconomics. In part I the authors first review the formal theory of dynamic optimization; they then present the numerical tools and econometric techniques necessary to evaluate the theoretical models. In language accessible to a reader with a limited background in econometrics, they explain most of the methods used in applied dynamic research today, from the estimation of probability in a coin flip to a complicated nonlinear stochastic structural model. These econometric techniques provide the final link between the dynamic programming problem and data. Part II is devoted to the application of dynamic programming to specific areas of applied economics, including the study of business cycles, consumption, and investment behavior. In each instance the authors present the specific optimization problem as a dynamic programming problem, characterize the optimal policy functions, estimate the parameters, and use models for policy evaluation. The original contribution of Dynamic Economics: Quantitative Methods and Applications lies in the integrated approach to the empirical application of dynamic optimization programming models. This integration shows that empirical applications actually complement the underlying theory of optimization, while dynamic programming problems provide needed structure for estimation and policy evaluation. |
| dynamic optimization book: Optimization in Economics and Finance Bruce D. Craven, Sardar M. N. Islam, 2005-10-24 Many optimization questions arise in economics and finance; an important example of this is the society's choice of the optimum state of the economy (the social choice problem). Optimization in Economics and Finance extends and improves the usual optimization techniques, in a form that may be adopted for modeling social choice problems. Problems discussed include: when is an optimum reached; when is it unique; relaxation of the conventional convex (or concave) assumptions on an economic model; associated mathematical concepts such as invex and quasimax; multiobjective optimal control models; and related computational methods and programs. These techniques are applied to economic growth models (including small stochastic perturbations), finance and financial investment models (and the interaction between financial and production variables), modeling sustainability over long time horizons, boundary (transversality) conditions, and models with several conflicting objectives. Although the applications are general and illustrative, the models in this book provide examples of possible models for a society's social choice for an allocation that maximizes welfare and utilization of resources. As well as using existing computer programs for optimization of models, a new computer program, named SCOM, is presented in this book for computing social choice models by optimal control. |
| dynamic optimization book: Anticipatory Optimization for Dynamic Decision Making Stephan Meisel, 2011-06-23 The availability of today’s online information systems rapidly increases the relevance of dynamic decision making within a large number of operational contexts. Whenever a sequence of interdependent decisions occurs, making a single decision raises the need for anticipation of its future impact on the entire decision process. Anticipatory support is needed for a broad variety of dynamic and stochastic decision problems from different operational contexts such as finance, energy management, manufacturing and transportation. Example problems include asset allocation, feed-in of electricity produced by wind power as well as scheduling and routing. All these problems entail a sequence of decisions contributing to an overall goal and taking place in the course of a certain period of time. Each of the decisions is derived by solution of an optimization problem. As a consequence a stochastic and dynamic decision problem resolves into a series of optimization problems to be formulated and solved by anticipation of the remaining decision process. However, actually solving a dynamic decision problem by means of approximate dynamic programming still is a major scientific challenge. Most of the work done so far is devoted to problems allowing for formulation of the underlying optimization problems as linear programs. Problem domains like scheduling and routing, where linear programming typically does not produce a significant benefit for problem solving, have not been considered so far. Therefore, the industry demand for dynamic scheduling and routing is still predominantly satisfied by purely heuristic approaches to anticipatory decision making. Although this may work well for certain dynamic decision problems, these approaches lack transferability of findings to other, related problems. This book has serves two major purposes: ‐ It provides a comprehensive and unique view of anticipatory optimization for dynamic decision making. Itfully integrates Markov decision processes, dynamic programming, data mining and optimization and introduces a new perspective on approximate dynamic programming. Moreover, the book identifies different degrees of anticipation, enabling an assessment of specific approaches to dynamic decision making. ‐ It shows for the first time how to successfully solve a dynamic vehicle routing problem by approximate dynamic programming. It elaborates on every building block required for this kind of approach to dynamic vehicle routing. Thereby the book has a pioneering character and is intended to provide a footing for the dynamic vehicle routing community. |
| dynamic optimization book: Dynamic Programming Richard Bellman, 2013-04-09 Introduction to mathematical theory of multistage decision processes takes a functional equation approach. Topics include existence and uniqueness theorems, optimal inventory equation, bottleneck problems, multistage games, Markovian decision processes, and more. 1957 edition. |
| dynamic optimization book: Applied Dynamic Programming for Optimization of Dynamical Systems Rush D. Robinett III, David G. Wilson, G. Richard Eisler, John E. Hurtado, 2005-01-01 Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized. |
| dynamic optimization book: Dynamic Optimization Arthur Earl Bryson, 1999 Dynamic Optimization takes an applied approach to its subject, offering many examples and solved problems that draw from aerospace, robotics, and mechanics. The abundance of thoroughly tested general algorithms and Matlab codes provide the reader with the practice necessary to master this inherently difficult subject, while the realistic engineering problems and examples keep the material interesting and relevant. FEATURES/BENEFITS Covers dynamic programming, relating it to the calculus of variations and optimal control, and neighboring optimum control (differential dynamic programming), a practical method for nonlinear feedback control. Includes a disk that contains 40 gradient and shooting codes, as well as codes that solve the time-varying Riccati equation (the DYNOPT Toolbox). These codes have been thoroughly tested on hundreds of problems. Contains many realistic examples and problems. Solutions to the examples and problems, as well as the codes that produce the figures, are included on the accompanying disk. Covers dynamic optimization with inequality constraints and singular arcs using inverse dynamic optimization (differential inclusion). |
| dynamic optimization book: Optimization in Economic Theory Avinash K. Dixit, 1990 A new edition of a student text which provides a broad study of optimization methods. It builds on the base of simple economic theory, elementary linear algebra and calculus, and reinforces each new mathematical idea by relating it to its economic application. |
| dynamic optimization book: Dynamic Programming Art Lew, Holger Mauch, 2006-10-09 This book provides a practical introduction to computationally solving discrete optimization problems using dynamic programming. From the examples presented, readers should more easily be able to formulate dynamic programming solutions to their own problems of interest. We also provide and describe the design, implementation, and use of a software tool that has been used to numerically solve all of the problems presented earlier in the book. |
| dynamic optimization book: Recursive Methods in Economic Dynamics Nancy L. Stokey, 1989-10-10 This rigorous but brilliantly lucid book presents a self-contained treatment of modern economic dynamics. Stokey, Lucas, and Prescott develop the basic methods of recursive analysis and illustrate the many areas where they can usefully be applied. |
| dynamic optimization book: Elements of Numerical Mathematical Economics with Excel Giovanni Romeo, 2019-11-28 Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization shows readers how to apply static and dynamic optimization theory in an easy and practical manner, without requiring the mastery of specific programming languages that are often difficult and expensive to learn. Featuring user-friendly numerical discrete calculations developed within the Excel worksheets, the book includes key examples and economic applications solved step-by-step and then replicated in Excel. After introducing the fundamental tools of mathematical economics, the book explores the classical static optimization theory of linear and nonlinear programming, applying the core concepts of microeconomics and some portfolio theory. This provides a background for the more challenging worksheet applications of the dynamic optimization theory. The book also covers special complementary topics such as inventory modelling, data analysis for business and economics, and the essential elements of Monte Carlo analysis. Practical and accessible, Elements of Numerical Mathematical Economics with Excel: Static and Dynamic Optimization increases the computing power of economists worldwide. This book is accompanied by a companion website that includes Excel examples presented in the book, exercises, and other supplementary materials that will further assist in understanding this useful framework. - Explains how Excel provides a practical numerical approach to optimization theory and analytics - Increases access to the economic applications of this universally-available, relatively simple software program - Encourages readers to go to the core of theoretical continuous calculations and learn more about optimization processes |
| dynamic optimization book: Dynamic Optimization , 2003 |
| dynamic optimization book: A First Course in Optimization Theory Rangarajan K. Sundaram, 1996-06-13 This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained. |
| dynamic optimization book: Dynamic Stochastic Optimization Kurt Marti, Yuri Ermoliev, Georg Ch. Pflug, 2012-12-06 Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective and constraint functions of dynamic stochastic optimization problems have the form of multidimensional integrals of rather involved in that may have a nonsmooth and even discontinuous character - the tegrands typical situation for hit-or-miss type of decision making problems involving irreversibility ofdecisions or/and abrupt changes ofthe system. In general, the exact evaluation of such functions (as is assumed in the standard optimization and control theory) is practically impossible. Also, the problem does not often possess the separability properties that allow to derive the standard in control theory recursive (Bellman) equations. |
| dynamic optimization book: Advanced Mathematics for Economists : Static and Dynamic Optimization Peter J. Lambert, 1985 |
| dynamic optimization book: Dynamic Optimization M.I. Kamien, 1998 |
| dynamic optimization book: Approximate Dynamic Programming for Dynamic Vehicle Routing Marlin Wolf Ulmer, 2018-05-09 This book provides a straightforward overview for every researcher interested in stochastic dynamic vehicle routing problems (SDVRPs). The book is written for both the applied researcher looking for suitable solution approaches for particular problems as well as for the theoretical researcher looking for effective and efficient methods of stochastic dynamic optimization and approximate dynamic programming (ADP). To this end, the book contains two parts. In the first part, the general methodology required for modeling and approaching SDVRPs is presented. It presents adapted and new, general anticipatory methods of ADP tailored to the needs of dynamic vehicle routing. Since stochastic dynamic optimization is often complex and may not always be intuitive on first glance, the author accompanies the ADP-methodology with illustrative examples from the field of SDVRPs. The second part of this book then depicts the application of the theory to a specific SDVRP. The process starts from the real-world application. The author describes a SDVRP with stochastic customer requests often addressed in the literature, and then shows in detail how this problem can be modeled as a Markov decision process and presents several anticipatory solution approaches based on ADP. In an extensive computational study, he shows the advantages of the presented approaches compared to conventional heuristics. To allow deep insights in the functionality of ADP, he presents a comprehensive analysis of the ADP approaches. |
| dynamic optimization book: Energy Optimization in Process Systems and Fuel Cells Stanislaw Sieniutycz, Jacek Jezowski, 2013-02-14 Energy Optimization in Process Systems and Fuel Cells, Second Edition covers the optimization and integration of energy systems, with a particular focus on fuel cell technology. With rising energy prices, imminent energy shortages, and increasing environmental impacts of energy production, energy optimization and systems integration is critically important. The book applies thermodynamics, kinetics and economics to study the effect of equipment size, environmental parameters, and economic factors on optimal power production and heat integration. Author Stanislaw Sieniutycz, highly recognized for his expertise and teaching, shows how costs can be substantially reduced, particularly in utilities common in the chemical industry. This second edition contains substantial revisions, with particular focus on the rapid progress in the field of fuel cells, related energy theory, and recent advances in the optimization and control of fuel cell systems. - New information on fuel cell theory, combined with the theory of flow energy systems, broadens the scope and usefulness of the book - Discusses engineering applications including power generation, resource upgrading, radiation conversion, and chemical transformation in static and dynamic systems - Contains practical applications of optimization methods that help solve the problems of power maximization and optimal use of energy and resources in chemical, mechanical, and environmental engineering |
| dynamic optimization book: Approximate Dynamic Programming Warren B. Powell, 2007-09-26 A complete and accessible introduction to the real-world applications of approximate dynamic programming With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems. Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming: Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts. |
| dynamic optimization book: Adaptive Dynamic Programming for Control Huaguang Zhang, Derong Liu, Yanhong Luo, Ding Wang, 2012-12-14 There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming in Discrete Time approaches the challenging topic of optimal control for nonlinear systems using the tools of adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods: • infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences; • finite-horizon control, implemented in discrete-time nonlinear systems showing the reader how to obtain suboptimal control solutions within a fixed number of control steps and with results more easily applied in real systems than those usually gained from infinite-horizon control; • nonlinear games for which a pair of mixed optimal policies are derived for solving games both when the saddle point does not exist, and, when it does, avoiding the existence conditions of the saddle point. Non-zero-sum games are studied in the context of a single network scheme in which policies are obtained guaranteeing system stability and minimizing the individual performance function yielding a Nash equilibrium. In order to make the coverage suitable for the student as well as for the expert reader, Adaptive Dynamic Programming in Discrete Time: • establishes the fundamental theory involved clearly with each chapter devoted to aclearly identifiable control paradigm; • demonstrates convergence proofs of the ADP algorithms to deepen understanding of the derivation of stability and convergence with the iterative computational methods used; and • shows how ADP methods can be put to use both in simulation and in real applications. This text will be of considerable interest to researchers interested in optimal control and its applications in operations research, applied mathematics computational intelligence and engineering. Graduate students working in control and operations research will also find the ideas presented here to be a source of powerful methods for furthering their study. |
| dynamic optimization book: Optimization Tools for Logistics Jean-Michel Réveillac, 2015-10-20 Optimization Tools for Logistics covers the theory and practice of the main principles of operational research and the ways it can be applied to logistics and decision support with regards to common software. The book is supported by worked problems and examples from industrial case studies, providing a comprehensive tool for readers from a variety of industries. - Covers simple explanations of the mathematical theories related to logistics - Contains many problems and examples from industrial case studies - Includes coverage of the use of readily available software; spreadsheets, project managers, flows simulators |
| dynamic optimization book: Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov, 2019-01-25 Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses. |
| dynamic optimization book: Optimization Jan Brinkhuis, Vladimir Tikhomirov, 2011-02-11 This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant. |
| dynamic optimization book: Applied Dynamic Programming Richard E. Bellman, Stuart E Dreyfus, 2015-12-08 This comprehensive study of dynamic programming applied to numerical solution of optimization problems. It will interest aerodynamic, control, and industrial engineers, numerical analysts, and computer specialists, applied mathematicians, economists, and operations and systems analysts. Originally published in 1962. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. |
| dynamic optimization book: From Shortest Paths to Reinforcement Learning Paolo Brandimarte, 2021-01-11 Dynamic programming (DP) has a relevant history as a powerful and flexible optimization principle, but has a bad reputation as a computationally impractical tool. This book fills a gap between the statement of DP principles and their actual software implementation. Using MATLAB throughout, this tutorial gently gets the reader acquainted with DP and its potential applications, offering the possibility of actual experimentation and hands-on experience. The book assumes basic familiarity with probability and optimization, and is suitable to both practitioners and graduate students in engineering, applied mathematics, management, finance and economics. |
| dynamic optimization book: Combinatorial Data Analysis Lawrence Hubert, Phipps Arabie, Jacqueline Meulman, 2001-01-01 Combinatorial data analysis (CDA) refers to a wide class of methods for the study of relevant data sets in which the arrangement of a collection of objects is absolutely central. The focus of this monograph is on the identification of arrangements, which are then further restricted to where the combinatorial search is carried out by a recursive optimization process based on the general principles of dynamic programming (DP). |
| dynamic optimization book: Evolutionary Optimization in Dynamic Environments Jürgen Branke, 2002 |
| dynamic optimization book: Optimal Control of Nonlinear Processes Dieter Grass, Jonathan P. Caulkins, Gustav Feichtinger, Gernot Tragler, Doris A. Behrens, 2008-07-24 Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site. |
| dynamic optimization book: Engineering Optimization Singiresu S. Rao, 1996-02-29 In Engineering Optimization, Professor Singiresu S. Rao provides an application-oriented presentation of the full array of classical and newly developed optimization techniques now being used by engineers in a wide range of industries. |
| dynamic optimization book: Stochastic Optimization Models In Finance (2006 Edition) William T Ziemba, Raymond G Vickson, 2006-09-11 A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems.Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever. |
| dynamic optimization book: Optimization Methods in Finance Gerard Cornuejols, Reha Tütüncü, 2006-12-21 Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses. |
DYNAMIC Definition & Meaning - Merriam-Webster
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Find 645 different ways to say DYNAMIC, along with antonyms, related words, and example sentences at Thesaurus.com.
DYNAMIC Definition & Meaning - Merriam-Webster
The meaning of DYNAMIC is marked by usually continuous and productive activity or change. How to use dynamic in a sentence.
DYNAMIC | English meaning - Cambridge Dictionary
DYNAMIC definition: 1. having a lot of ideas and enthusiasm: 2. continuously changing or developing: 3. relating to…. Learn more.
DYNAMIC Definition & Meaning | Dictionary.com
Dynamic definition: pertaining to or characterized by energy or effective action; vigorously active or forceful; energetic.. See examples of DYNAMIC used in a sentence.
DYNAMIC definition and meaning | Collins English Dictionary
The dynamic of a system or process is the force that causes it to change or progress. The dynamic of the market demands constant change and adjustment. Politics has its own dynamic.
Dynamic - definition of dynamic by The Free Dictionary
dynamic - characterized by action or forcefulness or force of personality; "a dynamic market"; "a dynamic speaker"; "the dynamic president of the firm"
What does dynamic mean? - Definitions.net
Dynamic is a term often used to refer to something that is constantly changing or evolving. It may also refer to an interaction or system characterized by constant change, activity, or progress. …
What Does Dynamic Mean? | The Word Counter
Apr 3, 2022 · Dictionary states that the word dynamic is an adjective that means energetic, forceful, or active. However, dynamic is used in a more specific way in the fields of physics …
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Dynamic Dental Wellness is a full spectrum dental office incorporating all aspects of modern technology. We offer the most comprehensive analysis and treatment options available for …
Dynamic Definition & Meaning | Britannica Dictionary
DYNAMIC meaning: 1 : always active or changing; 2 : having or showing a lot of energy
645 Synonyms & Antonyms for DYNAMIC - Thesaurus.com
Find 645 different ways to say DYNAMIC, along with antonyms, related words, and example sentences at Thesaurus.com.
