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First-Order Methods In Optimization, Amir Beck


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Автор: Amir Beck
Название:  First-Order Methods In Optimization
ISBN: 9781611974980
Издательство: Mare Nostrum (Eurospan)
Классификация:

ISBN-10: 1611974984
Обложка/Формат: Paperback
Страницы: 484
Вес: 1.02 кг.
Дата издания: 30.11.2017
Серия: Mos-siam series on optimization
Язык: English
Размер: 178 x 260 x 34
Читательская аудитория: Professional and scholarly
Ключевые слова: Applied mathematics,Mathematical theory of computation
Основная тема: Applied mathematics,Mathematical theory of computation
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Поставляется из: Англии
Описание: The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage.The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books.First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.
Дополнительное описание: Applied mathematics|Mathematical theory of computation


Mathematics for economics and  finance: methods and modelling

Автор: Anthony, M, , Biggs N.
Название: Mathematics for economics and finance: methods and modelling
ISBN: 0521559138 ISBN-13(EAN): 9780521559133
Издательство: Cambridge Academ
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Цена: 47510.00 T
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Описание: An introduction to mathematical modelling in economics and finance for students of both economics and mathematics. Throughout, the stress is firmly on how the mathematics relates to economics, illustrated with copious examples and exercises that will foster depth of understanding.

Optimization Theory and Methods

Автор: Wenyu Sun; Ya-Xiang Yuan
Название: Optimization Theory and Methods
ISBN: 144193765X ISBN-13(EAN): 9781441937650
Издательство: Springer
Цена: 121110.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Preface 1 Introduction 1.1 Introduction 1.2 Mathematics Foundations 1.2.1 Norm 1.2.2 Inverse and Generalized Inverse of a Matrix 1.2.3 Properties of Eigenvalues 1.2.4 Rank-One Update 1.2.5 Function and Differential 1.3 Convex Sets and Convex Functions 1.3.1 Convex Sets 1.3.2 Convex Functions 1.3.3 Separation and Support of Convex Sets 1.4 Optimality Conditions for Unconstrained Case 1.5 Structure of Optimization Methods Exercises 2 Line Search 2.1 Introduction 2.2 Convergence Theory for Exact Line Search 2.3 Section Methods 2.3.1 The Golden Section Method 2.3.2 The Fibonacci Method 2.4 Interpolation Method 2.4.1 Quadratic Interpolation Methods 2.4.2 Cubic Interpolation Method 2.5 Inexact Line Search Techniques 2.5.1 Armijo and Goldstein Rule 2.5.2 Wolfe-Powell Rule 2.5.3 Goldstein Algorithm and Wolfe-Powell Algorithm 2.5.4 Backtracking Line Search 2.5.5 Convergence Theorems of Inexact Line Search Exercises 3 Newton's Methods 3.1 The Steepest Descent Method 3.1.1 The Steepest Descent Method 3.1.2 Convergence of the Steepest Descent Method 3.1.3 Barzilai and Borwein Gradient Method 3.1.4 Appendix: Kantorovich Inequality 3.2 Newton's Method 3.3 Modified Newton's Method 3.4 Finite-Difference Newton's Method 3.5 Negative Curvature Direction Method 3.5.1 Gill-Murray Stable Newton's Method 3.5.2 Fiacco-McCormick Method 3.5.3 Fletcher-Freeman Method 3.5.4 Second-Order Step Rules 3.6 Inexact Newton's Method Exercises 4 Conjugate Gradient Method 4.1 Conjugate Direction Methods 4.2 Conjugate Gradient Method 4.2.1 Conjugate Gradient Method 4.2.2 Beale's Three-Term Conjugate Gradient Method 4.2.3 Preconditioned Conjugate Gradient Method 4.3 Convergence of Conjugate Gradient Methods 4.3.1 Global Convergence of Conjugate Gradient Methods 4.3.2 Convergence Rate of Conjugate Gradient Methods Exercises 5 Quasi-Newton Methods 5.1 Quasi-Newton Methods 5.1.1 Quasi-Newton Equation 5.1.2 Symmetric Rank-One (SR1) Update 5.1.3 DFP Update 5.1.4 BFGS Update and PSB Update 5.1.5 The Least Change Secant Update 5.2 The Broyden Class 5.3 Global Convergence of Quasi-Newton Methods 5.3.1 Global Convergence under Exact Line Search 5.3.2 Global Convergence under Inexact Line Search 5.4 Local Convergence of Quasi-Newton Methods 5.4.1 Superlinear Convergence of General Quasi-Newton Methods 5.4.2 Linear Convergence of General Quasi-Newton Methods 5.4.3 Local Convergence of Broyden's Rank-One Update 5.4.4 Local and Linear Convergence of DFP Method 5.4.5 Superlinear Convergence of BFGS Method 5.4.6 Superlinear Convergence of DFP Method 5.4.7 Local Convergence of Broyden's Class Methods 5.5 Self-Scaling Variable Metric (SSVM) Methods 5.5.1 Motivation to SSVM Method 5.5.2 Self-Scaling Variable Metric (SSVM) Method 5.5.3 Choices of the Scaling Factor 5.6 Sparse Quasi-Newton Methods 5.7 Limited Memory BFGS Method Exercises 6 Trust-Region and Conic Model Methods 6.1 Trust-Region Methods 6.1.1 Trust-Region Methods 6.1.2 Convergence of Trust-Region Methods 6.1.3 Solving A Trust-Region Subproblem 6.2 Conic Model and Collinear Scaling Algorithm 6.2.1 Conic Model 6.2.2 Generalized Quasi-Newton Equation 6.2.3 Updates that Preserve Past Information 6.2.4 Collinear Scaling BFGS Algorithm 6.3 Tensor Methods 6.3.1 Tensor Method for Nonlinear Equations 6.3.2 Tensor Methods for Unconstrained Optimization Exercises

Engineering Optimization: Applications, Methods an d Analysis

Автор: Rhinehart
Название: Engineering Optimization: Applications, Methods an d Analysis
ISBN: 1118936337 ISBN-13(EAN): 9781118936337
Издательство: Wiley
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Цена: 111880.00 T
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Описание:

An Application-Oriented Introduction to Essential Optimization Concepts and Best Practices

Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process.

Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project.

Examples, exercises, and homework throughout reinforce the author's "do, not study" approach to learning, underscoring the application-oriented discussion that provides a deep, generic understanding of the optimization process that can be applied to any field.

Providing excellent reference for students or professionals, Engineering Optimization

  • Describes and develops a variety of algorithms, including gradient based (such as Newton's, and Levenberg-Marquardt), direct search (such as Hooke-Jeeves, Leapfrogging, and Particle Swarm), along with surrogate functions for surface characterization
  • Provides guidance on optimizer choice by application, and explains how to determine appropriate optimizer parameter values
  • Details current best practices for critical stages of specifying an optimization procedure, including decision variables, defining constraints, and relationship modeling
  • Provides access to software and Visual Basic macros for Excel on the companion website, along with solutions to examples presented in the book

Clear explanations, explicit equation derivations, and practical examples make this book ideal for use as part of a class or self-study, assuming a basic understanding of statistics, calculus, computer programming, and engineering models. Anyone seeking best practices for "making the best choices" will find value in this introductory resource.



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