Modern Numerical Nonlinear Optimization
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Modern Numerical Nonlinear Optimization
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Author : Neculai Andrei
language : en
Publisher: Springer Nature
Release Date : 2022-10-18
Modern Numerical Nonlinear Optimization written by Neculai Andrei and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-18 with Mathematics categories.
This book includes a thorough theoretical and computational analysis of unconstrained and constrained optimization algorithms and combines and integrates the most recent techniques and advanced computational linear algebra methods. Nonlinear optimization methods and techniques have reached their maturity and an abundance of optimization algorithms are available for which both the convergence properties and the numerical performances are known. This clear, friendly, and rigorous exposition discusses the theory behind the nonlinear optimization algorithms for understanding their properties and their convergence, enabling the reader to prove the convergence of his/her own algorithms. It covers cases and computational performances of the most known modern nonlinear optimization algorithms that solve collections of unconstrained and constrained optimization test problems with different structures, complexities, as well as those with large-scale real applications. The book is addressed to all those interested in developing and using new advanced techniques for solving large-scale unconstrained or constrained complex optimization problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master in mathematical programming will find plenty of recent information and practical approaches for solving real large-scale optimization problems and applications.
Nonlinear Optimization
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Author : Andrzej Ruszczynski
language : en
Publisher: Princeton University Press
Release Date : 2011-09-19
Nonlinear Optimization written by Andrzej Ruszczynski and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-19 with Mathematics categories.
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.
Numerical Methods For Non Linear Optimization
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Author : F. A. Lootsma
language : en
Publisher:
Release Date : 1972
Numerical Methods For Non Linear Optimization written by F. A. Lootsma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Nonlinear Optimization
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Author : Francisco J. Aragón
language : en
Publisher: Springer
Release Date : 2019-02-27
Nonlinear Optimization written by Francisco J. Aragón and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.
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.
Linear And Nonlinear Optimization
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Author : Richard W. Cottle
language : en
Publisher: Springer
Release Date : 2017-06-11
Linear And Nonlinear Optimization written by Richard W. Cottle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-11 with Business & Economics categories.
This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia
Nonlinear Optimization
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Author : William P. Fox
language : en
Publisher: CRC Press
Release Date : 2020-12-08
Nonlinear Optimization written by William P. Fox and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-08 with Mathematics categories.
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
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Author : H. A. Eiselt
language : en
Publisher: Springer Nature
Release Date : 2019-11-09
Nonlinear Optimization written by H. A. Eiselt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-09 with Mathematics categories.
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.
Numerical Optimization 1984
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Author : Paul T. Boggs
language : en
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Release Date : 1985
Numerical Optimization 1984 written by Paul T. Boggs and has been published by Society for Industrial and Applied Mathematics (SIAM) this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Handbook Of Nature Inspired Optimization Algorithms The State Of The Art
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Author : Ali Mohamed
language : en
Publisher: Springer Nature
Release Date : 2022-08-31
Handbook Of Nature Inspired Optimization Algorithms The State Of The Art written by Ali Mohamed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-31 with Technology & Engineering categories.
The introduction of nature-inspired optimization algorithms (NIOAs), over the past three decades, helped solve nonlinear, high-dimensional, and complex computational optimization problems. NIOAs have been originally developed to overcome the challenges of global optimization problems such as nonlinearity, non-convexity, non-continuity, non-differentiability, and/or multimodality which traditional numerical optimization techniques had difficulties solving. The main objective for this book is to make available a self-contained collection of modern research addressing the general bound-constrained optimization problems in many real-world applications using nature-inspired optimization algorithms. This book is suitable for a graduate class on optimization, but will also be useful for interested senior students working on their research projects.
Linear And Nonlinear Programming
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Author : David G. Luenberger
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-07
Linear And Nonlinear Programming written by David G. Luenberger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-07 with Business & Economics categories.
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.