Nonlinear Optimization

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Nonlinear Optimization

Francisco J. Aragón,Miguel A. Goberna,Marco A. López,Margarita M.L. Rodríguez
Nonlinear Optimization Book PDF

Author : Francisco J. Aragón,Miguel A. Goberna,Marco A. López,Margarita M.L. Rodríguez
Publisher : Springer
Page : 350 pages
File Size : 41,8 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9783030111847

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Nonlinear Optimization by Francisco J. Aragón,Miguel A. Goberna,Marco A. López,Margarita M.L. Rodríguez Pdf

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 be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.

Nonlinear Optimization

Andrzej Ruszczynski
Nonlinear Optimization Book PDF

Author : Andrzej Ruszczynski
Publisher : Princeton University Press
Page : 464 pages
File Size : 44,8 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.

Introduction to Nonlinear Optimization

Amir Beck
Introduction to Nonlinear Optimization Book PDF

Author : Amir Beck
Publisher : SIAM
Page : 282 pages
File Size : 44,6 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.

Linear and Nonlinear Optimization

Igor Griva,Stephen G. Nash,Ariela Sofer
Linear and Nonlinear Optimization Book PDF

Author : Igor Griva,Stephen G. Nash,Ariela Sofer
Publisher : SIAM
Page : 742 pages
File Size : 41,5 Mb
Release : 2009-03-26
Category : Mathematics
ISBN : 9780898716610

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Linear and Nonlinear Optimization by Igor Griva,Stephen G. Nash,Ariela Sofer Pdf

Flexible graduate textbook that introduces the applications, theory, and algorithms of linear and nonlinear optimization in a clear succinct style, supported by numerous examples and exercises. It introduces important realistic applications and explains how optimization can address them.

Nonlinear Optimization

William P. Fox
Nonlinear Optimization Book PDF

Author : William P. Fox
Publisher : CRC Press
Page : 417 pages
File Size : 42,7 Mb
Release : 2020-12-08
Category : Mathematics
ISBN : 9781000196924

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Nonlinear Optimization by William P. Fox Pdf

Optimization is the act of obtaining the "best" result under given circumstances. In design, construction, and maintenance of any engineering system, engineers must make technological and managerial decisions to minimize either the effort or cost required or to maximize benefits. There is no single method available for solving all optimization problems efficiently. Several optimization methods have been developed for different types of problems. The optimum-seeking methods are mathematical programming techniques (specifically, nonlinear programming techniques). Nonlinear Optimization: Models and Applications presents the concepts in several ways to foster understanding. Geometric interpretation: is used to re-enforce the concepts and to foster understanding of the mathematical procedures. The student sees that many problems can be analyzed, and approximate solutions found before analytical solutions techniques are applied. Numerical approximations: early on, the student is exposed to numerical techniques. These numerical procedures are algorithmic and iterative. Worksheets are provided in Excel, MATLAB®, and MapleTM to facilitate the procedure. Algorithms: all algorithms are provided with a step-by-step format. Examples follow the summary to illustrate its use and application. Nonlinear Optimization: Models and Applications: Emphasizes process and interpretation throughout Presents a general classification of optimization problems Addresses situations that lead to models illustrating many types of optimization problems Emphasizes model formulations Addresses a special class of problems that can be solved using only elementary calculus Emphasizes model solution and model sensitivity analysis About the author: William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. He received his Ph.D. at Clemson University and has taught at the United States Military Academy and at Francis Marion University where he was the chair of mathematics. He has written many publications, including over 20 books and over 150 journal articles. Currently, he is an adjunct professor in the Department of Mathematics at the College of William and Mary. He is the emeritus director of both the High School Mathematical Contest in Modeling and the Mathematical Contest in Modeling.

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 : 55,5 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 with Engineering Applications

Michael Bartholomew-Biggs
Nonlinear Optimization with Engineering Applications Book PDF

Author : Michael Bartholomew-Biggs
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 54,7 Mb
Release : 2008-12-16
Category : Mathematics
ISBN : 9780387787237

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Nonlinear Optimization with Engineering Applications by Michael Bartholomew-Biggs Pdf

This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis. Chapters are self-contained with exercises provided at the end of most sections. Nonlinear Optimization with Engineering Applications is ideal for self-study and classroom use in engineering courses at the senior undergraduate or graduate level. The book will also appeal to postdocs and advanced researchers interested in the development and use of optimization algorithms.

Nonlinear Programming

Lorenz T. Biegler
Nonlinear Programming Book PDF

Author : Lorenz T. Biegler
Publisher : SIAM
Page : 411 pages
File Size : 50,5 Mb
Release : 2010-01-01
Category : Science
ISBN : 9780898719383

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Nonlinear Programming by Lorenz T. Biegler Pdf

This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.

Convex Analysis and Nonlinear Optimization

Jonathan Borwein,Adrian S. Lewis
Convex Analysis and Nonlinear Optimization Book PDF

Author : Jonathan Borwein,Adrian S. Lewis
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 40,5 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780387312569

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Convex Analysis and Nonlinear Optimization by Jonathan Borwein,Adrian S. Lewis Pdf

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Nonlinear Optimization in Finite Dimensions

Hubertus Th. Jongen,P. Jonker,F. Twilt
Nonlinear Optimization in Finite Dimensions Book PDF

Author : Hubertus Th. Jongen,P. Jonker,F. Twilt
Publisher : Springer Science & Business Media
Page : 516 pages
File Size : 49,5 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461500179

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Nonlinear Optimization in Finite Dimensions by Hubertus Th. Jongen,P. Jonker,F. Twilt Pdf

At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carried over to nonsmooth items, such as problems of Chebyshev approximation type. We made this choice in order to show that a good under standing of regular smooth problems may lead to a straightforward treatment of "just" continuous problems by means of suitable perturbation techniques, taking a priori nonsmoothness into account. Moreover, we make a focal point analysis in order to emphasize the difference between inner product norms and, for example, the maximum norm. Then, specific tools from algebraic topol ogy, in particular homology theory, are treated in some detail. However, this development is carried out only as far as it is needed to understand the relation between critical points of a function on a manifold with structured boundary. Then, we pay attention to three important subjects in nonlinear optimization.

Nonlinear Multiobjective Optimization

Kaisa Miettinen
Nonlinear Multiobjective Optimization Book PDF

Author : Kaisa Miettinen
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461555636

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Nonlinear Multiobjective Optimization by Kaisa Miettinen Pdf

Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.

Nonlinear Optimization Applications Using the GAMS Technology

Neculai Andrei
Nonlinear Optimization Applications Using the GAMS Technology Book PDF

Author : Neculai Andrei
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 44,5 Mb
Release : 2013-06-22
Category : Mathematics
ISBN : 9781461467977

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Nonlinear Optimization Applications Using the GAMS Technology by Neculai Andrei Pdf

Here is a collection of nonlinear optimization applications from the real world, expressed in the General Algebraic Modeling System (GAMS). The concepts are presented so that the reader can quickly modify and update them to represent real-world situations.

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 : 50,9 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.

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 : 40,5 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.

Combinatorial, Linear, Integer and Nonlinear Optimization Apps

J. MacGregor Smith
Combinatorial Linear Integer and Nonlinear Optimization Apps Book PDF

Author : J. MacGregor Smith
Publisher : Springer Nature
Page : 275 pages
File Size : 42,7 Mb
Release : 2021-10-17
Category : Mathematics
ISBN : 9783030758011

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Combinatorial, Linear, Integer and Nonlinear Optimization Apps by J. MacGregor Smith Pdf

This textbook provides an introduction to the use and understanding of optimization and modeling for upper-level undergraduate students in engineering and mathematics. The formulation of optimization problems is founded through concepts and techniques from operations research: Combinatorial Optimization, Linear Programming, and Integer and Nonlinear Programming (COLIN). Computer Science (CS) is also relevant and important given the applications of algorithms and Apps/algorithms (A) in solving optimization problems. Each chapter provides an overview of the main concepts of optimization according to COLINA, providing examples through App Inventor and AMPL software applications. All apps developed through the text are available for download. Additionally, the text includes links to the University of Wisconsin NEOS server, designed to handle more computing-intensive problems in complex optimization. Readers are encouraged to have some background in calculus, linear algebra, and related mathematics.