Numerical Methods For Constrained Optimization

Author : Juan Carlos De los Reyes
Publisher : Springer
Page : 123 pages
File Size : 43,9 Mb
Release : 2015-02-06
Category : Mathematics
ISBN : 9783319133959

Get Book

Numerical PDE-Constrained Optimization by Juan Carlos De los Reyes Pdf

This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

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 : 54,9 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015017289094

Get Book

Numerical Methods for Constrained Optimization by Philip E. Gill,P. E. Gill,William Allan Murray,Institute of Mathematics and Its Applications,National Physical Laboratory (Great Britain) Pdf

Author : Philip Edward Gill,W. Murray
Publisher : Unknown
Page : 0 pages
File Size : 54,8 Mb
Release : 1978
Category : Electronic
ISBN : OCLC:778055020

Get Book

Numerical Methods for Constrained Optimization by Philip Edward Gill,W. Murray Pdf

Author : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 53,6 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387227429

Get Book

Numerical Optimization by Jorge Nocedal,Stephen Wright Pdf

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 : W. Murray,P. E. Gill
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 1974
Category : Mathematical optimization
ISBN : OCLC:477009749

Get Book

Numerical Methods for Constrained Optimization by W. Murray,P. E. Gill Pdf

Author : J Gregory
Publisher : CRC Press
Page : 232 pages
File Size : 45,7 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351079310

Get Book

Constrained Optimization In The Calculus Of Variations and Optimal Control Theory by J Gregory Pdf

The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.

Author : Ernesto G. Birgin,JosŸ Mario Martinez
Publisher : SIAM
Page : 222 pages
File Size : 47,5 Mb
Release : 2014-04-30
Category : Mathematics
ISBN : 9781611973358

Get Book

Practical Augmented Lagrangian Methods for Constrained Optimization by Ernesto G. Birgin,JosŸ Mario Martinez Pdf

This book focuses on Augmented Lagrangian techniques for solving practical constrained optimization problems. The authors rigorously delineate mathematical convergence theory based on sequential optimality conditions and novel constraint qualifications. They also orient the book to practitioners by giving priority to results that provide insight on the practical behavior of algorithms and by providing geometrical and algorithmic interpretations of every mathematical result, and they fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.

Author : Emmanuel Laporte,Patrick Le Tallec
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461200697

Get Book

Numerical Methods in Sensitivity Analysis and Shape Optimization by Emmanuel Laporte,Patrick Le Tallec Pdf

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.

Author : Boris N. Pshenichnyj
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579189

Get Book

The Linearization Method for Constrained Optimization by Boris N. Pshenichnyj Pdf

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 : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 686 pages
File Size : 44,9 Mb
Release : 2006-12-11
Category : Mathematics
ISBN : 9780387400655

Get Book

Numerical Optimization by Jorge Nocedal,Stephen Wright Pdf

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 50,5 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209

Get Book

Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J. E. Dennis, Jr.,Robert B. Schnabel Pdf

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 : A. Bachem,M. Grötschel,B. Korte
Publisher : Springer Science & Business Media
Page : 662 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642688744

Get Book

Mathematical Programming The State of the Art by A. Bachem,M. Grötschel,B. Korte Pdf

In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.

Author : Mehiddin Al-Baali,Anton Purnama,Lucio Grandinetti
Publisher : Springer Nature
Page : 307 pages
File Size : 55,8 Mb
Release : 2021-12-01
Category : Mathematics
ISBN : 9783030720407

Get Book

Numerical Analysis and Optimization by Mehiddin Al-Baali,Anton Purnama,Lucio Grandinetti Pdf

This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry. Many real-world, complex problems can be formulated as optimization tasks, and can be characterized further as large scale, unconstrained, constrained, non-convex, nondifferentiable or discontinuous, and therefore require adequate computational methods, algorithms and software tools. These same tools are often employed by researchers working in current IT hot topics, such as big data, optimization and other complex numerical algorithms in the cloud, devising special techniques for supercomputing systems. This interdisciplinary view permeates the work included in this volume. The NAO conference series is held every three years at Sultan Qaboos University, with the aim of bringing together a group of international experts and presenting novel and advanced applications to facilitate interdisciplinary studies among pure scientific and applied knowledge. It is a venue where prominent scientists gather to share innovative ideas and know-how relating to new scientific methodologies, to promote scientific exchange, to discuss possible future cooperations, and to promote the mobility of local and young researchers.

Author : F. A. Lootsma
Publisher : Unknown
Page : 464 pages
File Size : 41,9 Mb
Release : 1972
Category : Mathematics
ISBN : UCAL:B4268455

Get Book

Numerical Methods for Non-linear Optimization by F. A. Lootsma Pdf

Author : Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 43,5 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9781402088391

Get Book

Optimization with PDE Constraints by Michael Hinze,Rene Pinnau,Michael Ulbrich,Stefan Ulbrich Pdf

Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.