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Author : F. A. Lootsma
Publisher : Unknown
Page : 464 pages
File Size : 50,9 Mb
Release : 1972
Category : Mathematical optimization
ISBN : UCAL:B4268455
Author : Philip E. Gill,P. E. Gill,William Allan Murray,Institute of Mathematics and Its Applications,National Physical Laboratory (Great Britain)
Publisher : Unknown
Page : 312 pages
File Size : 41,5 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015017289094
Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 52,8 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author : Margaret Ann Hagen Wright
Publisher : Unknown
Page : 552 pages
File Size : 54,5 Mb
Release : 1976
Category : Algorithms
ISBN : STANFORD:36105031717635
Author : Francisco J. Aragón,Miguel A. Goberna,Marco A. López,Margarita M.L. Rodríguez
Publisher : Springer
Page : 350 pages
File Size : 48,8 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9783030111847
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.
Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 48,7 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387227429
The new edition of this book presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on methods best suited to practical problems. This edition has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are widely used in practice and are the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience.
Author : Michael Bartholomew-Biggs
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 55,5 Mb
Release : 2008-12-16
Category : Mathematics
ISBN : 9780387787237
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.
Author : Boris N. Pshenichnyj
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579189
Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.
Author : Andrzej Ruszczynski
Publisher : Princeton University Press
Page : 464 pages
File Size : 49,7 Mb
Release : 2011-09-19
Category : Mathematics
ISBN : 9781400841059
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.
Author : Neculai Andrei
Publisher : Springer Nature
Page : 824 pages
File Size : 48,6 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9783031087202
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.
Author : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher : Unknown
Page : 36 pages
File Size : 51,5 Mb
Release : 1978
Category : Electronic
ISBN : STANFORD:36105046361700
The aim of this paper is to present a brief overview of current practice in solving nonlinearly constrained optimization problems. First, we consider selected theoretical and computational aspects of some of the widely used methods for such problems. Second, the status of implementations of such methods will be sketched. The latter discussion will include: factors to be considered in evaluating optimization programs; guidelines concerning the application of a general-purpose routine to any particular problem; and a list of some available software. (Author).
Author : Michael Bartholomew-Biggs
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 47,5 Mb
Release : 2006-07-21
Category : Mathematics
ISBN : 9780387241494
This instructive book introduces the key ideas behind practical nonlinear optimization, accompanied by computational examples and supporting software. It combines computational finance with an important class of numerical techniques.
Author : John T. Betts
Publisher : SIAM
Page : 748 pages
File Size : 41,7 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9781611976199
How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary differential equations and differential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge–Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.
Author : Wenyu Sun,Ya-Xiang Yuan
Publisher : Springer Science & Business Media
Page : 689 pages
File Size : 42,5 Mb
Release : 2006-08-06
Category : Mathematics
ISBN : 9780387249766
Optimization Theory and Methods can be used as a textbook for an optimization course for graduates and senior undergraduates. It is the result of the author's teaching and research over the past decade. It describes optimization theory and several powerful methods. For most methods, the book discusses an idea’s motivation, studies the derivation, establishes the global and local convergence, describes algorithmic steps, and discusses the numerical performance.
Author : Paul T. Boggs,Richard H. Byrd,Robert B. Schnabel
Publisher : SIAM
Page : 310 pages
File Size : 51,8 Mb
Release : 1985-01-01
Category : Mathematics
ISBN : 0898710545