Necessary Conditions for Infinite-horizon Discounted Two-stage Optimal Control Problems
Author: Miltos Makris
Publisher:
Published: 1998
Total Pages: 21
ISBN-13:
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Author: Miltos Makris
Publisher:
Published: 1998
Total Pages: 21
ISBN-13:
DOWNLOAD EBOOKAuthor: Michael Ralph Caputo
Publisher: Cambridge University Press
Published: 2005-01-17
Total Pages: 596
ISBN-13: 9780521603683
DOWNLOAD EBOOKFoundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.
Author: Atla Seierstad
Publisher:
Published: 1977
Total Pages: 15
ISBN-13:
DOWNLOAD EBOOKAuthor: Hubert Halkin
Publisher:
Published: 1972
Total Pages: 13
ISBN-13:
DOWNLOAD EBOOKIn a classical optimal control problem the terminal time, either prescribed a priori or not, is always a real number. In many dynamic optimization problems in economics one is lead to consider optimal control problems in which the terminal time is the extended real number + infinity. These are the so called optimal control problems with infinite horizon. In the paper the author gives a precise formulation for a standard problem of that type and establishes a necessary condition for that problem. (Author).
Author: Dieter Grass
Publisher: Springer Science & Business Media
Published: 2008-07-24
Total Pages: 552
ISBN-13: 3540776478
DOWNLOAD EBOOKDynamic 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.
Author: Josef L. Haunschmied
Publisher: Springer Nature
Published: 2020-11-07
Total Pages: 317
ISBN-13: 3030545768
DOWNLOAD EBOOKThis book presents the state of the art in the relatively new field of dynamic economic modelling with regime switches. The contributions, written by prominent scholars in the field, focus on dynamic decision problems with regime changes in underlying dynamics or objectives. Such changes can be externally driven or internally induced by decisions. Utilising the most advanced mathematical methods in optimal control and dynamic game theory, the authors address a broad range of topics, including capital accumulation, innovations, financial decisions, population economics, environmental and resource economics, institutional change and the dynamics of addiction. Given its scope, the book will appeal to all scholars interested in mathematical and quantitative economics.
Author: Atle Seierstad
Publisher:
Published: 1977
Total Pages: 15
ISBN-13: 9788257081027
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 2001
Total Pages: 1276
ISBN-13:
DOWNLOAD EBOOKAuthor: Dimitri Bertsekas
Publisher: Athena Scientific
Published: 2021-08-20
Total Pages: 498
ISBN-13: 1886529078
DOWNLOAD EBOOKThe purpose of this book is to develop in greater depth some of the methods from the author's Reinforcement Learning and Optimal Control recently published textbook (Athena Scientific, 2019). In particular, we present new research, relating to systems involving multiple agents, partitioned architectures, and distributed asynchronous computation. We pay special attention to the contexts of dynamic programming/policy iteration and control theory/model predictive control. We also discuss in some detail the application of the methodology to challenging discrete/combinatorial optimization problems, such as routing, scheduling, assignment, and mixed integer programming, including the use of neural network approximations within these contexts. The book focuses on the fundamental idea of policy iteration, i.e., start from some policy, and successively generate one or more improved policies. If just one improved policy is generated, this is called rollout, which, based on broad and consistent computational experience, appears to be one of the most versatile and reliable of all reinforcement learning methods. In this book, rollout algorithms are developed for both discrete deterministic and stochastic DP problems, and the development of distributed implementations in both multiagent and multiprocessor settings, aiming to take advantage of parallelism. Approximate policy iteration is more ambitious than rollout, but it is a strictly off-line method, and it is generally far more computationally intensive. This motivates the use of parallel and distributed computation. One of the purposes of the monograph is to discuss distributed (possibly asynchronous) methods that relate to rollout and policy iteration, both in the context of an exact and an approximate implementation involving neural networks or other approximation architectures. Much of the new research is inspired by the remarkable AlphaZero chess program, where policy iteration, value and policy networks, approximate lookahead minimization, and parallel computation all play an important role.
Author: Ivan Lirkov
Publisher: Springer
Published: 2009-03-26
Total Pages: 754
ISBN-13: 3540788271
DOWNLOAD EBOOKCoverage in this proceedings volume includes robust multilevel and hierarchical preconditioning methods, applications for large scale computations and optimization of coupled engineering problems, and applications of metaheuristics to large-scale problems.