Coverart for item
The Resource Nonlinear optimization, Andrzej Ruszczyński, (electronic resource)

Nonlinear optimization, Andrzej Ruszczyński, (electronic resource)

Label
Nonlinear optimization
Title
Nonlinear optimization
Statement of responsibility
Andrzej Ruszczyński
Creator
Contributor
Subject
Language
eng
Summary
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.--
Assigning source
Provided by Publisher
Cataloging source
NhCcYBP
http://library.link/vocab/creatorName
Ruszczyński, Andrzej P
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
ProQuest (Firm)
Series statement
ProQuest Ebook Central
http://library.link/vocab/subjectName
  • Mathematical optimization
  • Nonlinear theories
Label
Nonlinear optimization, Andrzej Ruszczyński, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://ebookcentral.proquest.com/lib/EUI/detail.action?docID=768547
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 431-444) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface xi Chapter 1. Introduction 1 PART 1. THEORY 15 Chapter 2. Elements of Convex Analysis 17 2.1 Convex Sets 17 2.2 Cones 25 2.3 Extreme Points 39 2.4 Convex Functions 44 2.5 Subdifferential Calculus 57 2.6 Conjugate Duality 75 Chapter 3. Optimality Conditions 88 3.1 Unconstrained Minima of Differentiable Functions 88 3.2 Unconstrained Minima of Convex Functions 92 3.3 Tangent Cones 98 3.4 Optimality Conditions for Smooth Problems 113 3.5 Optimality Conditions for Convex Problems 125 3.6 Optimality Conditions for Smooth-Convex Problems 133 3.7 Second Order Optimality Conditions 139 3.8 Sensitivity 150 Chapter 4. Lagrangian Duality 160 4.1 The Dual Problem 160 4.2 Duality Relations 166 4.3 Conic Programming 175 4.4 Decomposition 180 4.5 Convex Relaxation of Nonconvex Problems 186 4.6 The Optimal Value Function 191 4.7 The Augmented Lagrangian 196 PART 2. METHODS 209 Chapter 5. Unconstrained Optimization of Differentiable Functions 211 5.1 Introduction to Iterative Algorithms 211 5.2 Line Search 213 5.3 The Method of Steepest Descent 218 5.4 Newton's Method 233 5.5 The Conjugate Gradient Method 240 5.6 Quasi-Newton Methods 257 5.7 Trust Region Methods 266 5.8 Nongradient Methods 275 Chapter 6. Constrained Optimization of Differentiable Functions 286 6.1 Feasible Point Methods 286 6.2 Penalty Methods 297 6.3 The Basic Dual Method 308 6.4 The Augmented Lagrangian Method 311 6.5 Newton's Method 324 6.6 Barrier Methods 331 Chapter 7. Nondifferentiable Optimization 343 7.1 The Subgradient Method 343 7.2 The Cutting Plane Method 357 7.3 The Proximal Point Method 366 7.4 The Bundle Method 372 7.5 The Trust Region Method 384 7.6 Constrained Problems 389 7.7 Composite Optimization 397 7.8 Nonconvex Constraints 406 Appendix A. Stability of Set-Constrained Systems 411 A.1 Linear-Conic Systems 411 A.2 Set-Constrained Linear Systems 415 A.3 Set-Constrained Nonlinear Systems 418 Further Reading 427 Bibliography 431 Index 445
Control code
ybp7078913
Dimensions
unknown
Extent
1 online resource (xii, 448 pages)
Form of item
online
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781400841059
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other physical details
illustrations.
Specific material designation
remote
System control number
(OCoLC)948773077
Label
Nonlinear optimization, Andrzej Ruszczyński, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://ebookcentral.proquest.com/lib/EUI/detail.action?docID=768547
Publication
Bibliography note
Includes bibliographical references (pages 431-444) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
Preface xi Chapter 1. Introduction 1 PART 1. THEORY 15 Chapter 2. Elements of Convex Analysis 17 2.1 Convex Sets 17 2.2 Cones 25 2.3 Extreme Points 39 2.4 Convex Functions 44 2.5 Subdifferential Calculus 57 2.6 Conjugate Duality 75 Chapter 3. Optimality Conditions 88 3.1 Unconstrained Minima of Differentiable Functions 88 3.2 Unconstrained Minima of Convex Functions 92 3.3 Tangent Cones 98 3.4 Optimality Conditions for Smooth Problems 113 3.5 Optimality Conditions for Convex Problems 125 3.6 Optimality Conditions for Smooth-Convex Problems 133 3.7 Second Order Optimality Conditions 139 3.8 Sensitivity 150 Chapter 4. Lagrangian Duality 160 4.1 The Dual Problem 160 4.2 Duality Relations 166 4.3 Conic Programming 175 4.4 Decomposition 180 4.5 Convex Relaxation of Nonconvex Problems 186 4.6 The Optimal Value Function 191 4.7 The Augmented Lagrangian 196 PART 2. METHODS 209 Chapter 5. Unconstrained Optimization of Differentiable Functions 211 5.1 Introduction to Iterative Algorithms 211 5.2 Line Search 213 5.3 The Method of Steepest Descent 218 5.4 Newton's Method 233 5.5 The Conjugate Gradient Method 240 5.6 Quasi-Newton Methods 257 5.7 Trust Region Methods 266 5.8 Nongradient Methods 275 Chapter 6. Constrained Optimization of Differentiable Functions 286 6.1 Feasible Point Methods 286 6.2 Penalty Methods 297 6.3 The Basic Dual Method 308 6.4 The Augmented Lagrangian Method 311 6.5 Newton's Method 324 6.6 Barrier Methods 331 Chapter 7. Nondifferentiable Optimization 343 7.1 The Subgradient Method 343 7.2 The Cutting Plane Method 357 7.3 The Proximal Point Method 366 7.4 The Bundle Method 372 7.5 The Trust Region Method 384 7.6 Constrained Problems 389 7.7 Composite Optimization 397 7.8 Nonconvex Constraints 406 Appendix A. Stability of Set-Constrained Systems 411 A.1 Linear-Conic Systems 411 A.2 Set-Constrained Linear Systems 415 A.3 Set-Constrained Nonlinear Systems 418 Further Reading 427 Bibliography 431 Index 445
Control code
ybp7078913
Dimensions
unknown
Extent
1 online resource (xii, 448 pages)
Form of item
online
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781400841059
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other physical details
illustrations.
Specific material designation
remote
System control number
(OCoLC)948773077

Library Locations

    • Badia FiesolanaBorrow it
      Via dei Roccettini 9, San Domenico di Fiesole, 50014, IT
      43.803074 11.283055
Processing Feedback ...