Network Optimization Continuous And Discrete Models
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Network Optimization Continuous And Discrete Models
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 1998-01-01
Network Optimization Continuous And Discrete Models written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Business & Economics categories.
An insightful, comprehensive, and up-to-date treatment of linear, nonlinear, and discrete/combinatorial network optimization problems, their applications, and their analytical and algorithmic methodology. It covers extensively theory, algorithms, and applications, and it aims to bridge the gap between linear and nonlinear network optimization on one hand, and integer/combinatorial network optimization on the other. It complements several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Introduction to Linear Optimization (Athena Scientific, 1997), Nonlinear Programming (Athena Scientific, 1999), as well as our other book on the subject of network optimization Network Flows and Monotropic Optimization (Athena Scientific, 1998).
Network Optimization Methods In Passivity Based Cooperative Control
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Author : Miel Sharf
language : en
Publisher: Springer Nature
Release Date : 2021-05-24
Network Optimization Methods In Passivity Based Cooperative Control written by Miel Sharf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Technology & Engineering categories.
This book establishes an important mathematical connection between cooperative control problems and network optimization problems. It shows that many cooperative control problems can in fact be understood, under certain passivity assumptions, using a pair of static network optimization problems. Merging notions from passivity theory and network optimization, it describes a novel network optimization approach that can be applied to the synthesis of controllers for diffusively-coupled networks of passive (or passivity-short) dynamical systems. It also introduces a data-based, model-free approach for the synthesis of network controllers for multi-agent systems with passivity-short agents. Further, the book describes a method for monitoring link faults in multi-agent systems using passivity theory and graph connectivity. It reports on some practical case studies describing the effectivity of the developed approaches in vehicle networks. All in all, this book offers an extensive source of information and novel methods in the emerging field of multi-agent cooperative control, paving the way to future developments of autonomous systems for various application domains
Network Optimization
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Author : Julia Pahl
language : en
Publisher: Springer
Release Date : 2011-09-15
Network Optimization written by Julia Pahl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-15 with Computers categories.
This book constitutes the refereed proceedings of the 5th International Conference on Network Optimization, INOC 2011, held in Hamburg, Germany, in June 2011. The 65 revised full papers presented were carefully reviewed and selected from numerous submissions. The papers highlight recent developments in network optimization and are organized in the following topical sections: theoretical problems, uncertainty, graph theory and network design; network flows; routing and transportation; and further optimization problems and applications (energy oriented network design, telecom applications, location, maritime shipping, and graph theory).
Time Varying Network Optimization
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Author : Dan Sha
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-05
Time Varying Network Optimization written by Dan Sha 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 2007-05-05 with Computers categories.
Network ?ow optimization problems may arise in a wide variety of important ?elds, such as transportation, telecommunication, computer networking, ?nancial planning, logistics and supply chain management, energy systems, etc. Signi?cant and elegant results have been achieved onthetheory,algorithms,andapplications,ofnetwork?owoptimization in the past few decades; See, for example, the seminal books written by Ahuja, Magnanti and Orlin (1993), Bazaraa, Jarvis and Sherali (1990), Bertsekas (1998), Ford and Fulkerson (1962), Gupta (1985), Iri (1969), Jensen and Barnes (1980), Lawler (1976), and Minieka (1978). Most network optimization problems that have been studied up to date are, however, static in nature, in the sense that it is assumed that it takes zero time to traverse any arc in a network and that all attributes of the network are constant without change at any time. Networks in the real world are, nevertheless, time-varying in essence, in which any ?ow must take a certain amount of time to traverse an arc and the network structure and parameters (such as arc and node capacities) may change over time. In such a problem, how to plan and control the transmission of ?ow becomes very important, since waiting at a node, or travelling along a particular arc with di?erent speed, may allow one to catch the best timing along his path, and therefore achieve his overall objective, such as a minimum overall cost or a minimum travel time from the origin to the destination.
Algorithms And Models For Network Data And Link Analysis
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Author : François Fouss
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-12
Algorithms And Models For Network Data And Link Analysis written by François Fouss and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-12 with Computers categories.
A hands-on, entry-level guide to algorithms for extracting information about social and economic behavior from network data.
Convex Analysis And Optimization
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2003-03-01
Convex Analysis And Optimization written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-01 with Mathematics categories.
A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. The book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2016), Network Optimization (Athena Scientific, 1998), and Introduction to Linear Optimization (Athena Scientific, 1997). Aside from a thorough account of convex analysis and optimization, the book aims to restructure the theory of the subject, by introducing several novel unifying lines of analysis, including: 1) A unified development of minimax theory and constrained optimization duality as special cases of duality between two simple geometrical problems. 2) A unified development of conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization. 3) A unification of the major constraint qualifications allowing the use of Lagrange multipliers for nonconvex constrained optimization, using the notion of constraint pseudonormality and an enhanced form of the Fritz John necessary optimality conditions. Among its features the book: a) Develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar b) Provides a geometric, highly visual treatment of convex and nonconvex optimization problems, including existence of solutions, optimality conditions, Lagrange multipliers, and duality c) Includes an insightful and comprehensive presentation of minimax theory and zero sum games, and its connection with duality d) Describes dual optimization, the associated computational methods, including the novel incremental subgradient methods, and applications in linear, quadratic, and integer programming e) Contains many examples, illustrations, and exercises with complete solutions (about 200 pages) posted at the publisher's web site http://www.athenasc.com/convexity.html
Abstract Dynamic Programming
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2022-01-01
Abstract Dynamic Programming written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This is the 3rd edition of a research monograph providing a synthesis of old research on the foundations of dynamic programming (DP), with the modern theory of approximate DP and new research on semicontractive models. It aims at a unified and economical development of the core theory and algorithms of total cost sequential decision problems, based on the strong connections of the subject with fixed point theory. The analysis focuses on the abstract mapping that underlies DP and defines the mathematical character of the associated problem. The discussion centers on two fundamental properties that this mapping may have: monotonicity and (weighted sup-norm) contraction. It turns out that the nature of the analytical and algorithmic DP theory is determined primarily by the presence or absence of these two properties, and the rest of the problem's structure is largely inconsequential. New research is focused on two areas: 1) The ramifications of these properties in the context of algorithms for approximate DP, and 2) The new class of semicontractive models, exemplified by stochastic shortest path problems, where some but not all policies are contractive. The 3rd edition is very similar to the 2nd edition, except for the addition of a new chapter (Chapter 5), which deals with abstract DP models for sequential minimax problems and zero-sum games, The book is an excellent supplement to several of our books: Neuro-Dynamic Programming (Athena Scientific, 1996), Dynamic Programming and Optimal Control (Athena Scientific, 2017), Reinforcement Learning and Optimal Control (Athena Scientific, 2019), and Rollout, Policy Iteration, and Distributed Reinforcement Learning (Athena Scientific, 2020).
Dynamic Programming And Optimal Control
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2012-10-23
Dynamic Programming And Optimal Control written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-23 with Mathematics categories.
This is the leading and most up-to-date textbook on the far-ranging algorithmic methodology of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. Among its special features, the book 1) provides a unifying framework for sequential decision making, 2) treats simultaneously deterministic and stochastic control problems popular in modern control theory and Markovian decision popular in operations research, 3) develops the theory of deterministic optimal control problems including the Pontryagin Minimum Principle, 4) introduces recent suboptimal control and simulation-based approximation techniques (neuro-dynamic programming), which allow the practical application of dynamic programming to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model, 5) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume.
Reinforcement Learning And Optimal Control
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2019-07-01
Reinforcement Learning And Optimal Control written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-01 with Computers categories.
This book considers large and challenging multistage decision problems, which can be solved in principle by dynamic programming (DP), but their exact solution is computationally intractable. We discuss solution methods that rely on approximations to produce suboptimal policies with adequate performance. These methods are collectively known by several essentially equivalent names: reinforcement learning, approximate dynamic programming, neuro-dynamic programming. They have been at the forefront of research for the last 25 years, and they underlie, among others, the recent impressive successes of self-learning in the context of games such as chess and Go. Our subject has benefited greatly from the interplay of ideas from optimal control and from artificial intelligence, as it relates to reinforcement learning and simulation-based neural network methods. One of the aims of the book is to explore the common boundary between these two fields and to form a bridge that is accessible by workers with background in either field. Another aim is to organize coherently the broad mosaic of methods that have proved successful in practice while having a solid theoretical and/or logical foundation. This may help researchers and practitioners to find their way through the maze of competing ideas that constitute the current state of the art. This book relates to several of our other books: Neuro-Dynamic Programming (Athena Scientific, 1996), Dynamic Programming and Optimal Control (4th edition, Athena Scientific, 2017), Abstract Dynamic Programming (2nd edition, Athena Scientific, 2018), and Nonlinear Programming (Athena Scientific, 2016). However, the mathematical style of this book is somewhat different. While we provide a rigorous, albeit short, mathematical account of the theory of finite and infinite horizon dynamic programming, and some fundamental approximation methods, we rely more on intuitive explanations and less on proof-based insights. Moreover, our mathematical requirements are quite modest: calculus, a minimal use of matrix-vector algebra, and elementary probability (mathematically complicated arguments involving laws of large numbers and stochastic convergence are bypassed in favor of intuitive explanations). The book illustrates the methodology with many examples and illustrations, and uses a gradual expository approach, which proceeds along four directions: (a) From exact DP to approximate DP: We first discuss exact DP algorithms, explain why they may be difficult to implement, and then use them as the basis for approximations. (b) From finite horizon to infinite horizon problems: We first discuss finite horizon exact and approximate DP methodologies, which are intuitive and mathematically simple, and then progress to infinite horizon problems. (c) From deterministic to stochastic models: We often discuss separately deterministic and stochastic problems, since deterministic problems are simpler and offer special advantages for some of our methods. (d) From model-based to model-free implementations: We first discuss model-based implementations, and then we identify schemes that can be appropriately modified to work with a simulator. The book is related and supplemented by the companion research monograph Rollout, Policy Iteration, and Distributed Reinforcement Learning (Athena Scientific, 2020), which focuses more closely on several topics related to rollout, approximate policy iteration, multiagent problems, discrete and Bayesian optimization, and distributed computation, which are either discussed in less detail or not covered at all in the present book. The author's website contains class notes, and a series of videolectures and slides from a 2021 course at ASU, which address a selection of topics from both books.
Rollout Policy Iteration And Distributed Reinforcement Learning
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2021-08-20
Rollout Policy Iteration And Distributed Reinforcement Learning written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-20 with Computers categories.
The 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.