This extensive rigorous texbook, developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, discrete-time optimal control, and large-scale optimization 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet Much supplementary/support material can be found at the book's web page

Nonlinear Programming

Science & Math

Dimitri P. Bertsekas

Bertsekas, Dimitri P.

Mathematics

Athena Scientific

This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. Among its special features, the book: 1) Quantifies the performance of parallel algorithms, including the limitations imposed by the communication and synchronization penalties. 2) Describes communication algorithms for a variety of system architectures including tree, mesh, and hypercube. 3) Provides a comprehensive convergence analysis of asynchronous methods and a comparison with their asynchronous counterparts. 4) Cove

Parallel and Distributed Computation: Numerical Methods (Optimization and Neural Computation)

John Tsitsiklis

Tsitsiklis, John

Computers & Technology

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. Among its special features, the book: 1) provides a comprehensive account of the principal algorithms for linear network flow problems, including simplex, dual ascent, and auction algorithms 2) describes the application of network algorithms in many practical contexts, with special emphasis on data communication networks 3) develops in detail the computational complexity analysis of the main linear network optimization algorithms 4) covers extensively the main algorithms for specialized network problems, such as shortest path, max-flow, assignment, and traveling salesman 5) describes the main models for discrete network optimization problems, such as constrained shortest path, traveling salesman, vehicle routing, multidimensional assignment, facility location, spanning tree construction, etc 6) describes the main algorithmic approaches for integer-constrained network problems, such as branch-and-bound, Lagrangian relaxation and subgradient optimization, genetic algorithms, tabu search, simulated annealing, and rollout algorithms 7) develops the main methods for nonlinear network problems, such as convex separable and multicommodity flow problems arising in communication, transportation, and manufacturing contexts 8) discusses extensively auction algorithms, based on the author's original research on the subject 9) contains many examples, practical applications, illustrations, and exercises 10) contains much new material not found in any other textbook

Network Optimization: Continuous and Discrete Models (Optimization, Computation, and Control)

Certification

This research monograph is the authoritative and comprehensive treatment of the mathematical foundations of stochastic optimal control of discrete-time systems, including the treatment of the intricate measure-theoretic issues.

Stochastic Optimal Control: The Discrete-Time Case (Optimization and Neural Computation Series)

Steven E. Shreve

Shreve, Steven E.

This widely referenced textbook, first published in 1982 by Academic Press, is the authoritative and comprehensive treatment of some of the most widely used constrained optimization methods, including the augmented Lagrangian/multiplier and sequential quadratic programming methods. Among its special features, the book: 1) treats extensively augmented Lagrangian methods, including an exhaustive analysis of the associated convergence and rate of convergence properties 2) develops comprehensively sequential quadratic programming and other Lagrangian methods 3) provides a detailed analysis of differentiable and nondifferentiable exact penalty methods 4) presents nondifferentiable and minimax optimization methods based on smoothing 5) contains much in depth research not found in any other textbook

Constrained Optimization and Lagrange Multiplier Methods (Optimization and neural computation series)

The third edition of the book is a thoroughly rewritten version of the 1999 2nd edition. New material was included, some of the old material was discarded, and a large portion of the remainder was reorganized or revised. This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book was developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, large-scale optimization, signal processing, machine learning, and optimal control 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet. Much supplementary/support material can be found at the publisher's and the author's web sites

A rigorous and comprehensive treatment of network flow theory and monotropic optimization by one of the world's most renowned applied mathematicians. This classic textbook, first published by J. Wiley &amp; Sons, Inc., in 1984, covers extensively the duality theory and the algorithms of linear and nonlinear network optimization optimization, and their significant extensions to monotropic programming (separable convex constrained optimization problems, including linear programs). Monotropic programming problems are characterized by a rich interplay between combinatorial structure and convexity properties. Rockafellar develops, for the first time, algorithms and a remarkably complete duality theory for these problems.

Network Flows and Monotropic Optimization

Rockafellar, R. Tyrrell

This is a monograph at the forefront of research on reinforcement learning, also referred to by other names such as approximate dynamic programming and neuro-dynamic programming. It 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. Among others, it can be applied on-line using easily implementable simulation, and it can be used for discrete deterministic combinatorial optimization, as well as for stochastic Markov decision problems. 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. Several of the ideas that we develop in some depth in this monograph have been central in the implementation of recent high profile successes, such as the AlphaZero program for playing chess, Go, and other games. In addition to the fundamental process of successive policy iteration/improvement, this program includes the use of deep neural networks for representation of both value functions and policies, the extensive use of large scale parallelization, and the simplification of lookahead minimization, through methods involving Monte Carlo tree search and pruning of the lookahead tree. In this monograph, we also focus on policy iteration, value and policy neural network representations, parallel and distributed computation, and lookahead simplification. Thus while there are significant differences, the principal design ideas that form the core of this monograph are shared by the AlphaZero architecture, except that we develop these ideas in a broader and less application-specific framework. Among its special features, the book: a) Presents new research relating to distributed asynchronous computation, partitioned architectures, and multiagent systems, with application to challenging large scale optimization problems, such as combinatorial/discrete optimization, as well as partially observed Markov decision problems. b) Describes variants of rollout and policy iteration for problems with a multiagent structure, which allow a dramatic reduction of the computational requirements for lookahead minimization. c) Establishes a connection of rollout with model predictive control, one of the most prominent control system design methodologies. d) Expands the coverage of some research areas discussed in 2019 textbook Reinforcement Learning and Optimal Control by the same author. See the author's website for selected sections, instructional videos and slides, and other supporting material.

Rollout, Policy Iteration, and Distributed Reinforcement Learning

Dimitri Bertsekas

A two-volume set, consisting of the latest editions of the two volumes (4th edition (2017) for Vol. I, and 4th edition (2012) for Vol. II). Much supplementary material can be found at the book's web page. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use, as well as an up-to-date account of some of the most interesting developments in approximate dynamic programming. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides a detailed account of approximate large-scale dynamic programming and reinforcement learning. This is a textbook on the far-ranging algorithmic methododogy 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 introduction to the methodology of Neuro-Dynamic Programming, which is the focus of much recent research.

Dynamic Programming and Optimal Control

Computer Science

This is a substantially expanded (by about 30%) and improved edition of Vol. 1 of the best-selling dynamic programming book by Bertsekas. (A relatively minor revision of Vol.\ 2 is planned for the second half of 2001.) DP is a central algorithmic method for optimal control, sequential decision making under uncertainty, and combinatorial optimization. The treatment focuses on basic unifying themes and conceptual foundations. It illustrates the power of the method with many examples and applications from engineering, operations research, and economics. 
Among its special features, the book: 
(a) provides a unifying framework for sequential decision making 
(b) develops the theory of deterministic optimal control including the Pontryagin Minimum Principle 
(c) describes neuro-dynamic programming techniques for practical application of DP to complex problems that involve the dual curse of large dimension and lack of an accurate mathematical model 
(d) provides a comprehensive treatment of infinite horizon problems in the second volume, and an introductory treatment in the first volume 
(e) contains many exercises, with solutions of the most theoretical ones posted on the book's www page 
Highlights of the revision: (a) Much new material on suboptimal control, including neuro-dynamic programming and rollout algorithms, and their applications in combinatorial optimization and stochastic optimal control. (b) A section on estimation and control of systems with a non-probabilistic (set membership) description of uncertainty. (c) A section on infinite horizon continuous-time (semi-Markov) decision problems. (d) A new appendix dealing with the minimax and expected utility approaches for formulating decision problems under uncertainty.

Dynamic Programming and Optimal Control, Vol. 1 (Optimization and Computation Series)

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Books by Athena Scientific

See the best price to sell, buy or rent books by the Athena Scientific publisher. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Nonlinear Programming

Parallel and Distributed Computation: Numerical Methods (Optimization and Neural Computation)

Network Optimization: Continuous and Discrete Models (Optimization, Computation, and Control)

Stochastic Optimal Control: The Discrete-Time Case (Optimization and Neural Computation Series)

Constrained Optimization and Lagrange Multiplier Methods (Optimization and neural computation series)

Nonlinear Programming

Network Flows and Monotropic Optimization

Rollout, Policy Iteration, and Distributed Reinforcement Learning

Dynamic Programming and Optimal Control

Dynamic Programming and Optimal Control, Vol. 1 (Optimization and Computation Series)