Stochastic Recursive Algorithms for Optimization

In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures wit

Focusing on algorithms for distributed-memory parallel architectures, Parallel Algorithms presents a rigorous yet accessible treatment of theoretical models of parallel computation, parallel algorithm

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decad

Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decad

This book introduces the new experimentalism in evolutionary computation, providing tools to understand algorithms and programs and their interaction with optimization problems. It develops and applie

Once again, Robert Sedgewick provides a current and comprehensive introduction to important algorithms. The focus this time is on graph algorithms, which are increasingly critical for a wide range of

A unique interdisciplinary foundation for real-world problem solvingStochastic search and optimization techniques are used in a vast number of areas, including aerospace, medicine, transportation, and

Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical en

Outstanding text for graduate students and researchers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating

Once again, Robert Sedgewick provides a current and comprehensive introduction to important algorithms. The focus this time is on graph algorithms, which are increasingly critical for a wide range of

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

This second edition takes account of latest developments in optimization theory and practice. New material includes a discussion of trust region and convex approximation algorithms, how to construct o

The first complete guide to using the Stochastic Finite Element Method for reliability assessmentUnlike other analytical reliability estimation techniques, the Stochastic Finite Element Method (SFEM)

Ideal for courses aiming to give examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models. It introduces the methods of probability model building

Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION"This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best a

The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows. The classical theory was initiated by K. Itô and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby Itô's theory as a special case. The book can be used with advanced courses on probability theory or for self-study. The author begins with a discussion of Markov processes, martingales and Brownian motion, followed by a review of Itô's stochastic analysis. The next chapter deals with continuous semimartingales with spatial parameters, in order to study stochastic flow, and a generalisation of Ito's equation. Stochastic flows and their relation with this are generalised and considered in chapter 4. It is shown that solutions of a g

This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics and computer s

This volume is an introduction to stochastic processes and their statistics. Basic stochastic processes are developed from real world situations to the need for generating mathematical models, while a

This volume considers the regularity theory of solutions to stochastic differential equations, and the existence of stochastic flows, Regularity properties are one of the main tools for the analysis o

For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. This tutorial presents the basic concepts in the design and analysis of randomized algorithms. The first part of the book presents tools from probability theory and probabilistic analysis that are recurrent in algorithmic applications. Algorithmic examples are given to illustrate the use of each tool in a concrete setting. In the second part of the book, each of the seven chapters focuses on one important area of application of randomized algorithms: data structures; geometric algorithms; graph algorithms; number theory; enumeration; parallel algorithms; and on-line algorithms. A comprehensive and representative selection of the algorithms in these areas is also given. This book should prove invaluable as a reference for researchers and professional programmers, as well as for students.

Covering deterministic scheduling, stochastic scheduling, and the probabilistic analysis of algorithms, this unusually broad view of the subject brings together tutorials, surveys and articles with or

Stochastic partial differential equations can be used in many areas of science to model complex systems that evolve over time. Their analysis is currently an area of much research interest. This book consists of papers given at the ICMS Edinburgh meeting held in 1994 on this topic, and it brings together some of the world's best known authorities on stochastic partial differential equations. Subjects covered include the stochastic Navier–Stokes equation, critical branching systems, population models, statistical dynamics, and ergodic properties of Markov semigroups. For all workers on stochastic partial differential equations this book will have much to offer.

This hypermedia CD-ROM provides an ideal format for the visual explanation of complex algorithms contained in the text Introduction to Algorithms, by Thomas H. Cormen, Charles E. Leiserson, and Ronal

This textbook for first year graduate courses (usually called Stochastic Processes, Applied Probability, or Stochastic Modeling) is subtitled, The random world of Happy Harry, and is filled with exa

This rigorous but brilliantly lucid book presents a self-contained treatment of modern economic dynamics. Stokey, Lucas, and Prescott develop the basic methods of recursive analysis and illustrate th

1.Covers not only AI theory, but modern applications e.g., game programming, machine learning, swarming, artificial immune systems, genetic algorithms, pattern recognition, numerical optimization, dat

A high school student can create deep Q-learning code to control her robot, without any understanding of the meaning of 'deep' or 'Q', or why the code sometimes fails. This book is designed to explain the science behind reinforcement learning and optimal control in a way that is accessible to students with a background in calculus and matrix algebra. A unique focus is algorithm design to obtain the fastest possible speed of convergence for learning algorithms, along with insight into why reinforcement learning sometimes fails. Advanced stochastic process theory is avoided at the start by substituting random exploration with more intuitive deterministic probing for learning. Once these ideas are understood, it is not difficult to master techniques rooted in stochastic control. These topics are covered in the second part of the book, starting with Markov chain theory and ending with a fresh look at actor-critic methods for reinforcement learning.

A unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB®'s optimization toolbox, and to link MATLAB's results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS® for design optimization. A wide variety of optimization problems are covered including con

This book focuses on sequences as recursive relations and then transitions to periodic recursive patterns and eventually periodic recursive patterns. The aim of the author is to get students to unders

The relatively young theory of structured dependence between stochastic processes has many real-life applications in areas including finance, insurance, seismology, neuroscience, and genetics. With this monograph, the first to be devoted to the modeling of structured dependence between random processes, the authors not only meet the demand for a solid theoretical account but also develop a stochastic processes counterpart of the classical copula theory that exists for finite-dimensional random variables. Presenting both the technical aspects and the applications of the theory, this is a valuable reference for researchers and practitioners in the field, as well as for graduate students in pure and applied mathematics programs. Numerous theoretical examples are included, alongside examples of both current and potential applications, aimed at helping those who need to model structured dependence between dynamic random phenomena.

The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.

This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may

This book presents a unified framework for the tractable analysis of large-scale, multi-antenna wireless networks using stochastic geometry. This mathematical analysis is essential for assessing and u

The book covers control and filtering problems for several classes of stochastic networked systems including stability, robustness, reliability, consensus performance, and/or disturbance attenuation l

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-

This book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashi

This book introduces readers to the background, general framework, main operators, and other basic characteristics of biogeography-based optimization (BBO), which is an emerging branch of bio-inspired

Algorithms and Applications for Academic Search, Recommendation and Quantitative Association Rule Mining presents novel algorithms for academic search, recommendation and association rule mining that