Download or read book Approximation of Optimal Solutions for Infinite Horizon Linear Programs written by Richard C. Grinold and published by . This book was released on 1974 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper defines infinite horizon linear programs and presents a procedure that will approximate the optimal solution of almost any infinite horizon linear program that has a finite optimal value. In addition, it is demonstrated that other procedures for calculating optimal solutions will not, in general, approximate the optimal solution.

Download or read book Approximating Solutions in Infinite Horizon Optimization written by William Paul Cross and published by . This book was released on 1995 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Evaluating End Effects for Linear and Integer Programs Using Infinite horizon Linear Programming written by Steven C. Walker and published by . This book was released on 1995 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacement/modemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving (or approximately solving) infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions.

Download or read book Evaluating End Effects for Linear and Integer Programs Using Infinite horizon Linear Programming written by Steven C. Walker and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation considers optimization problems in which similar decisions need to be made repeatedly over many successive periods. These problems have wide applications including manpower planning, scheduling, production planning and control, capacity expansion, and equipment replacement/modemization. In reality these decision problems usually extend over an indeterminate horizon, but it is common practice to model them using a finite horizon. Unfortunately, an artificial finite horizon may adversely influence optimal decisions, a difficulty commonly referred to as the end effects problem. Past research into end effects has focused on theoretical issues associated with solving (or approximately solving) infinite-horizon extensions of finite-horizon problems. This dissertation derives equivalent finite-horizon formulations for a small class of infinite-horizon problem structures. For a larger class of problems, it also develops finite-horizon approximations which bound the infinite- horizon optimal solution, thereby quantifying the influence of end effects. For linear programs, extensions of these approximations quantify the end effects of fixed initial period decisions over a functional range of future infinite-horizon conditions.

Download or read book solution approximation in infinite horizon linear quadratic control written by irwin e. schochetman and published by . This book was released on 1991 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approximate Dynamic Programming written by Warren B. Powell and published by John Wiley & Sons. This book was released on 2007-10-05 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Linear Optimization and Approximation written by K. Glashoff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: A linear optimization problem is the task of minimizing a linear real-valued function of finitely many variables subject to linear con straints; in general there may be infinitely many constraints. This book is devoted to such problems. Their mathematical properties are investi gated and algorithms for their computational solution are presented. Applications are discussed in detail. Linear optimization problems are encountered in many areas of appli cations. They have therefore been subject to mathematical analysis for a long time. We mention here only two classical topics from this area: the so-called uniform approximation of functions which was used as a mathematical tool by Chebyshev in 1853 when he set out to design a crane, and the theory of systems of linear inequalities which has already been studied by Fourier in 1823. We will not treat the historical development of the theory of linear optimization in detail. However, we point out that the decisive break through occurred in the middle of this century. It was urged on by the need to solve complicated decision problems where the optimal deployment of military and civilian resources had to be determined. The availability of electronic computers also played an important role. The principal computational scheme for the solution of linear optimization problems, the simplex algorithm, was established by Dantzig about 1950. In addi tion, the fundamental theorems on such problems were rapidly developed, based on earlier published results on the properties of systems of linear inequalities.

Download or read book An Approximation Framework for Infinite Horizon Optimization Problems in a Mathematical Programming Setting written by International Business Machines Corporation. Research Division and published by . This book was released on 1999 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Dynamic optimization problems, including optimal control problems, have typically relied on the solution techniques of dynamic programming, involving the sequential solution of certain optimality equations. However, many problems cannot be handled this way, due to complex constraints, a continuous state space, and other complicating factors. When recast as mathematical programs relying on the powerful tools of optimization, especially duality, and decomposability to deal with very large problems, the boundaries imposed by dynamic programming are lifted. This paper develops approximation techniques for stationary infinite horizon problems with discounted costs, in the framework of mathematical programming. A reference is given for parallel results for stochastic dynamic optimization problems."

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1988 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Programming in Infinite dimensional Spaces written by Edward J. Anderson and published by John Wiley & Sons. This book was released on 1987 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite-dimensional linear programs; Algebraic fundamentals; Topology and duality. Semi-infinite linear programs; The mass-transfer problem; Maximal flow in a dynamic network; Continuous linear programs; Other infinite linear programs; Index.

Download or read book Neural Approximations for Optimal Control and Decision written by Riccardo Zoppoli and published by Springer Nature. This book was released on 2019-12-17 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: • a general functional optimization framework; • thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; • comparison of classical and neural-network based methods of approximate solution; • bounds to the errors of approximate solutions; • solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; • applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and • numerous, numerically detailed examples. The authors’ diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.

Download or read book Linear Semi Infinite Optimization written by Miguel A. Goberna and published by . This book was released on 1998-03-11 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.

Download or read book Inverse Optimization in Countably Infinite Linear Programs written by Archis Ghate and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given the objective coefficients and a feasible solution for a linear program, inverse optimization involves finding a new vector of objective coefficients that (i) is as close as possible to the original vector; and (ii) would make the given feasible solution optimal. This problem is well-studied for finite-dimensional linear programs. We develop a duality-based inverse optimization framework for countably infinite linear programs (CILPs) -- problems that include a countably infinite number of variables and constraints. Using the standard weighted absolute sum metric to quantify distance between cost vectors, we provide conditions under which constraints in the inverse optimization problem can be reformulated as a countably infinite set of linear constraints. We propose a convergent algorithm to solve the resulting infinite-dimensional mathematical program. This algorithm involves solving a sequence of finite-dimensional linear programs. We apply these results to inverse optimization in infinite-horizon non-stationary Markov decision processes.

Download or read book EXISTENCE AND DISCOVERY OF AVERAGE OPTIMAL SOLUTIONS IN DETERMINISTIC INFINTTE HORIZON OPTIMIZATION written by and published by . This book was released on 1997 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Compilation of Theses Abstracts October 1994 September 1995 written by United States. Naval Postgraduate School, Monterey, CA. and published by . This book was released on 1995 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Method for Computing an Optimal Solution to an Infinite horizon Dynamic Leontief Model with Substitution written by Stanford University. Department of Operations Research. Operations Research House and published by . This book was released on 1971 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Reinforcement Learning and Optimal Control written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2019-07-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.