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Numerical Methods For Stochastic Optimization
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Book Synopsis Numerical Methods for Stochastic Control Problems in Continuous Time by : Harold Kushner
Download or read book Numerical Methods for Stochastic Control Problems in Continuous Time written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.
Book Synopsis Numerical Solution of Stochastic Differential Equations by : Peter E. Kloeden
Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Book Synopsis Numerical Techniques for Stochastic Optimization by : Yuri Ermoliev
Download or read book Numerical Techniques for Stochastic Optimization written by Yuri Ermoliev and published by Springer. This book was released on 2011-10-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rapid changes in today's environment emphasize the need for models and meth ods capable of dealing with the uncertainty inherent in virtually all systems re lated to economics, meteorology, demography, ecology, etc. Systems involving interactions between man, nature and technology are subject to disturbances which may be unlike anything which has been experienced in the past. In the technological revolution increases uncertainty-as each new stage particular, perturbs existing knowledge of structures, limitations and constraints. At the same time, many systems are often too complex to allow for precise measure ment of the parameters or the state of the system. Uncertainty, nonstationarity, disequilibrium are pervasivE' characteristics of most modern systems. In order to manage such situations (or to survive in such an environment) we must develop systems which can facilitate oar response to uncertainty and changing conditions. In our individual behavior we often follow guidelines that are conditioned by the need to be prepared for all (likely) eventualities: insur ance, wearing seat·belts, savings versus investments, annual medical check.ups, even keeping an umbrella at the office, etc. One can identify two major types of mechanisms: the short term adaptive adjustments (defensive driving, mar keting, inventory control, etc.) that are made after making some observations of the system's parameters, and the long term anticipative actions (engineer ing design, policy setting, allocation of resources, investment strategies, etc.).
Book Synopsis First-order and Stochastic Optimization Methods for Machine Learning by : Guanghui Lan
Download or read book First-order and Stochastic Optimization Methods for Machine Learning written by Guanghui Lan and published by Springer Nature. This book was released on 2020-05-15 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.
Book Synopsis Stochastic Optimization by : Johannes Schneider
Download or read book Stochastic Optimization written by Johannes Schneider and published by Springer Science & Business Media. This book was released on 2007-08-06 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.
Book Synopsis Stochastic Optimization Methods by : Kurt Marti
Download or read book Stochastic Optimization Methods written by Kurt Marti and published by Springer. This book was released on 2015-02-21 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
Book Synopsis Stochastic Multi-Stage Optimization by : Pierre Carpentier
Download or read book Stochastic Multi-Stage Optimization written by Pierre Carpentier and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
Book Synopsis Numerical Optimization by : Jorge Nocedal
Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Book Synopsis Lectures on Stochastic Programming by : Alexander Shapiro
Download or read book Lectures on Stochastic Programming written by Alexander Shapiro and published by SIAM. This book was released on 2009-01-01 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.
Book Synopsis Monte-Carlo Methods and Stochastic Processes by : Emmanuel Gobet
Download or read book Monte-Carlo Methods and Stochastic Processes written by Emmanuel Gobet and published by CRC Press. This book was released on 2016-09-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from the author’s course at the Ecole Polytechnique, Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear focuses on the simulation of stochastic processes in continuous time and their link with partial differential equations (PDEs). It covers linear and nonlinear problems in biology, finance, geophysics, mechanics, chemistry, and other application areas. The text also thoroughly develops the problem of numerical integration and computation of expectation by the Monte-Carlo method. The book begins with a history of Monte-Carlo methods and an overview of three typical Monte-Carlo problems: numerical integration and computation of expectation, simulation of complex distributions, and stochastic optimization. The remainder of the text is organized in three parts of progressive difficulty. The first part presents basic tools for stochastic simulation and analysis of algorithm convergence. The second part describes Monte-Carlo methods for the simulation of stochastic differential equations. The final part discusses the simulation of non-linear dynamics.
Book Synopsis Stochastic Approximation Methods for Constrained and Unconstrained Systems by : H.J. Kushner
Download or read book Stochastic Approximation Methods for Constrained and Unconstrained Systems written by H.J. Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. Such recu- sive algorithms occur frequently in stochastic and adaptive control and optimization theory and in statistical esti- tion theory. Typically, a sequence {X } of estimates of a n parameter is obtained by means of some recursive statistical th st procedure. The n estimate is some function of the n_l estimate and of some new observational data, and the aim is to study the convergence, rate of convergence, and the pa- metric dependence and other qualitative properties of the - gorithms. In this sense, the theory is a statistical version of recursive numerical analysis. The approach taken involves the use of relatively simple compactness methods. Most standard results for Kiefer-Wolfowitz and Robbins-Monro like methods are extended considerably. Constrained and unconstrained problems are treated, as is the rate of convergence problem. While the basic method is rather simple, it can be elaborated to allow a broad and deep coverage of stochastic approximation like problems. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design. It is often possible to obtain an intuitive understanding of algorithm behavior or qualitative dependence upon parameters, etc., without getting involved in a great deal of deta~l.
Book Synopsis Sequential Stochastic Optimization by : R. Cairoli
Download or read book Sequential Stochastic Optimization written by R. Cairoli and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequential Stochastic Optimization provides mathematicians andapplied researchers with a well-developed framework in whichstochastic optimization problems can be formulated and solved.Offering much material that is either new or has never beforeappeared in book form, it lucidly presents a unified theory ofoptimal stopping and optimal sequential control of stochasticprocesses. This book has been carefully organized so that littleprior knowledge of the subject is assumed; its only prerequisitesare a standard graduate course in probability theory and somefamiliarity with discrete-parameter martingales. Major topics covered in Sequential Stochastic Optimization include: * Fundamental notions, such as essential supremum, stopping points,accessibility, martingales and supermartingales indexed by INd * Conditions which ensure the integrability of certain suprema ofpartial sums of arrays of independent random variables * The general theory of optimal stopping for processes indexed byInd * Structural properties of information flows * Sequential sampling and the theory of optimal sequential control * Multi-armed bandits, Markov chains and optimal switching betweenrandom walks
Book Synopsis Convex and Stochastic Optimization by : J. Frédéric Bonnans
Download or read book Convex and Stochastic Optimization written by J. Frédéric Bonnans and published by Springer. This book was released on 2019-04-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with. The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules. This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis Stochastic Optimization Methods by : Kurt Marti
Download or read book Stochastic Optimization Methods written by Kurt Marti and published by Springer Science & Business Media. This book was released on 2008-05-16 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems arising in practice involve random model parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insenistive with respect to random parameter variations, appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, differentiation formulas for probabilities and expectations.
Book Synopsis Stochastic Global Optimization Methods and Applications to Chemical, Biochemical, Pharmaceutical and Environmental Processes by : Ch. Venkateswarlu
Download or read book Stochastic Global Optimization Methods and Applications to Chemical, Biochemical, Pharmaceutical and Environmental Processes written by Ch. Venkateswarlu and published by Elsevier. This book was released on 2019-11-18 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic global optimization methods and applications to chemical, biochemical, pharmaceutical and environmental processes presents various algorithms that include the genetic algorithm, simulated annealing, differential evolution, ant colony optimization, tabu search, particle swarm optimization, artificial bee colony optimization, and cuckoo search algorithm. The design and analysis of these algorithms is studied by applying them to solve various base case and complex optimization problems concerning chemical, biochemical, pharmaceutical, and environmental engineering processes. Design and implementation of various classical and advanced optimization strategies to solve a wide variety of optimization problems makes this book beneficial to graduate students, researchers, and practicing engineers working in multiple domains. This book mainly focuses on stochastic, evolutionary, and artificial intelligence optimization algorithms with a special emphasis on their design, analysis, and implementation to solve complex optimization problems and includes a number of real applications concerning chemical, biochemical, pharmaceutical, and environmental engineering processes.
Book Synopsis Numerical Methods in Finance and Economics by : Paolo Brandimarte
Download or read book Numerical Methods in Finance and Economics written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.