Introduction To Nonlinear Optimization

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Introduction to Nonlinear Optimization

Amir Beck
Introduction to Nonlinear Optimization Book PDF

Author : Amir Beck
Publisher : SIAM
Page : 282 pages
File Size : 40,9 Mb
Release : 2014-10-27
Category : Mathematics
ISBN : 9781611973655

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Introduction to Nonlinear Optimization by Amir Beck Pdf

This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.

First-Order Methods in Optimization

Amir Beck
First Order Methods in Optimization Book PDF

Author : Amir Beck
Publisher : SIAM
Page : 476 pages
File Size : 41,8 Mb
Release : 2017-10-02
Category : Mathematics
ISBN : 9781611974980

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First-Order Methods in Optimization by Amir Beck Pdf

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.

Introduction to Non-linear Optimization

L. E. Scales
Introduction to Non linear Optimization Book PDF

Author : L. E. Scales
Publisher : Unknown
Page : 243 pages
File Size : 53,9 Mb
Release : 1985
Category : Mathematical optimization
ISBN : 0333325524

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Introduction to Non-linear Optimization by L. E. Scales Pdf

In this textbook the author concentrates on presenting the main core of methods in non-linear optimization that have evolved over the past two decades. It is intended primarily for actual or potential practising optimizer who need to know how different methods work, how to select methods for the job in hand and how to use the chosen method. While the level of mathematical rigour is not very high, the book necessarily contains a considerable amount of mathematical argument and pre-supposes a knowledge such as would be attained by someone reaching the end of the second year of an undergraduate course in physical science, engineering or computational mathematics. The main emphasis is on linear algebra, and more advanced topics are discussed briefly where relevant in the text. The book will appeal to a range of students and research workers working on optimization problems in such fields as applied mathematics, computer science, engineering, business studies, economics and operations research.

Introduction to the Theory of Nonlinear Optimization

Johannes Jahn
Introduction to the Theory of Nonlinear Optimization Book PDF

Author : Johannes Jahn
Publisher : Springer Nature
Page : 325 pages
File Size : 42,9 Mb
Release : 2020-07-02
Category : Business & Economics
ISBN : 9783030427603

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Introduction to the Theory of Nonlinear Optimization by Johannes Jahn Pdf

This book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Introduction to Nonlinear and Global Optimization

Eligius M.T. Hendrix,Boglárka G.-Tóth
Introduction to Nonlinear and Global Optimization Book PDF

Author : Eligius M.T. Hendrix,Boglárka G.-Tóth
Publisher : Springer
Page : 208 pages
File Size : 44,5 Mb
Release : 2010-04-27
Category : Mathematics
ISBN : 9780387886701

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Introduction to Nonlinear and Global Optimization by Eligius M.T. Hendrix,Boglárka G.-Tóth Pdf

This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization which includes the presentation of numerous algorithms, examples, and illustrations, designed to improve the reader’s intuition and develop the analytical skills needed to identify optimization problems, classify the structure of a model, and determine whether a solution fulfills optimality conditions.

An Introduction to Nonlinear Optimization Theory

Marius Durea,Radu Strugariu
An Introduction to Nonlinear Optimization Theory Book PDF

Author : Marius Durea,Radu Strugariu
Publisher : Walter de Gruyter GmbH & Co KG
Page : 328 pages
File Size : 47,8 Mb
Release : 2014-01-01
Category : Mathematics
ISBN : 9783110427356

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An Introduction to Nonlinear Optimization Theory by Marius Durea,Radu Strugariu Pdf

The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.

Introduction to Nonlinear Optimization

Amir Beck
Introduction to Nonlinear Optimization Book PDF

Author : Amir Beck
Publisher : SIAM
Page : 286 pages
File Size : 46,7 Mb
Release : 2014-10-27
Category : Mathematics
ISBN : 9781611973648

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Introduction to Nonlinear Optimization by Amir Beck Pdf

This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.

Nonlinear Optimization

H. A. Eiselt,Carl-Louis Sandblom
Nonlinear Optimization Book PDF

Author : H. A. Eiselt,Carl-Louis Sandblom
Publisher : Springer Nature
Page : 366 pages
File Size : 52,8 Mb
Release : 2019-11-09
Category : Mathematics
ISBN : 9783030194628

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Nonlinear Optimization by H. A. Eiselt,Carl-Louis Sandblom Pdf

This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.

Nonlinear Optimization

Andrzej Ruszczynski
Nonlinear Optimization Book PDF

Author : Andrzej Ruszczynski
Publisher : Princeton University Press
Page : 464 pages
File Size : 55,9 Mb
Release : 2011-09-19
Category : Mathematics
ISBN : 9781400841059

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Nonlinear Optimization by Andrzej Ruszczynski Pdf

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.

Nonlinear Programming

Peter Zörnig
Nonlinear Programming Book PDF

Author : Peter Zörnig
Publisher : Walter de Gruyter GmbH & Co KG
Page : 360 pages
File Size : 51,5 Mb
Release : 2014-08-22
Category : Mathematics
ISBN : 9783110372519

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Nonlinear Programming by Peter Zörnig Pdf

This book is an introduction to nonlinear programming. It deals with the theoretical foundations and solution methods, beginning with the classical procedures and reaching up to “modern” methods like trust region methods or procedures for nonlinear and global optimization. A comprehensive bibliography including diverse web sites with information about nonlinear programming, in particular software, is presented. Without sacrificing the necessary mathematical rigor, excessive formalisms are avoided. Several examples, exercises with detailed solutions, and applications are provided, making the text adequate for individual studies. The book is written for students from the fields of applied mathematics, engineering, economy, and computation.

Introduction to Nonlinear Optimization

Amir Beck
Introduction to Nonlinear Optimization Book PDF

Author : Amir Beck
Publisher : SIAM
Page : 364 pages
File Size : 47,9 Mb
Release : 2023-06-29
Category : Mathematics
ISBN : 9781611977622

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Introduction to Nonlinear Optimization by Amir Beck Pdf

Built on the framework of the successful first edition, this book serves as a modern introduction to the field of optimization. The author’s objective is to provide the foundations of theory and algorithms of nonlinear optimization as well as to present a variety of applications from diverse areas of applied sciences. Introduction to Nonlinear Optimization gradually yet rigorously builds connections between theory, algorithms, applications, and actual implementation. The book contains several topics not typically included in optimization books, such as optimality conditions in sparsity constrained optimization, hidden convexity, and total least squares. Readers will discover a wide array of applications such as circle fitting, Chebyshev center, the Fermat–Weber problem, denoising, clustering, total least squares, and orthogonal regression. These applications are studied both theoretically and algorithmically, illustrating concepts such as duality. Python and MATLAB programs are used to show how the theory can be implemented. The extremely popular CVX toolbox (MATLAB) and CVXPY module (Python) are described and used. More than 250 theoretical, algorithmic, and numerical exercises enhance the reader's understanding of the topics. (More than 70 of the exercises provide detailed solutions, and many others are provided with final answers.) The theoretical and algorithmic topics are illustrated by Python and MATLAB examples. This book is intended for graduate or advanced undergraduate students in mathematics, computer science, electrical engineering, and potentially other engineering disciplines.

Nonlinear Programming

Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Nonlinear Programming Book PDF

Author : Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty
Publisher : John Wiley & Sons
Page : 867 pages
File Size : 52,8 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781118626306

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Nonlinear Programming by Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty Pdf

COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.

An Introduction to Optimization

Edwin K. P. Chong,Stanislaw H. Żak
An Introduction to Optimization Book PDF

Author : Edwin K. P. Chong,Stanislaw H. Żak
Publisher : John Wiley & Sons
Page : 497 pages
File Size : 49,6 Mb
Release : 2004-04-05
Category : Mathematics
ISBN : 9780471654001

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An Introduction to Optimization by Edwin K. P. Chong,Stanislaw H. Żak Pdf

A modern, up-to-date introduction to optimization theory and methods This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Linear and Nonlinear Programming

David G. Luenberger,Yinyu Ye
Linear and Nonlinear Programming Book PDF

Author : David G. Luenberger,Yinyu Ye
Publisher : Springer Science & Business Media
Page : 546 pages
File Size : 47,9 Mb
Release : 2008-06-20
Category : Business & Economics
ISBN : 9780387745039

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Linear and Nonlinear Programming by David G. Luenberger,Yinyu Ye Pdf

This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California’s Stanford University, who has written lots of extra material including some on Interior Point Methods.

Introduction to Applied Optimization

Urmila Diwekar
Introduction to Applied Optimization Book PDF

Author : Urmila Diwekar
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 45,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475737455

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Introduction to Applied Optimization by Urmila Diwekar Pdf

This text presents a multi-disciplined view of optimization, providing students and researchers with a thorough examination of algorithms, methods, and tools from diverse areas of optimization without introducing excessive theoretical detail. This second edition includes additional topics, including global optimization and a real-world case study using important concepts from each chapter. Introduction to Applied Optimization is intended for advanced undergraduate and graduate students and will benefit scientists from diverse areas, including engineers.