Constrained Optimization And Lagrange Multiplier Methods

Author : Dimitri P. Bertsekas
Publisher : Academic Press
Page : 412 pages
File Size : 54,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483260471

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Constrained Optimization and Lagrange Multiplier Methods by Dimitri P. Bertsekas Pdf

Computer Science and Applied Mathematics: Constrained Optimization and Lagrange Multiplier Methods focuses on the advancements in the applications of the Lagrange multiplier methods for constrained minimization. The publication first offers information on the method of multipliers for equality constrained problems and the method of multipliers for inequality constrained and nondifferentiable optimization problems. Discussions focus on approximation procedures for nondifferentiable and ill-conditioned optimization problems; asymptotically exact minimization in the methods of multipliers; duality framework for the method of multipliers; and the quadratic penalty function method. The text then examines exact penalty methods, including nondifferentiable exact penalty functions; linearization algorithms based on nondifferentiable exact penalty functions; differentiable exact penalty functions; and local and global convergence of Lagrangian methods. The book ponders on the nonquadratic penalty functions of convex programming. Topics include large scale separable integer programming problems and the exponential method of multipliers; classes of penalty functions and corresponding methods of multipliers; and convergence analysis of multiplier methods. The text is a valuable reference for mathematicians and researchers interested in the Lagrange multiplier methods.

Author : Kazufumi Ito,Karl Kunisch
Publisher : SIAM
Page : 359 pages
File Size : 53,6 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 0898718619

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Lagrange Multiplier Approach to Variational Problems and Applications by Kazufumi Ito,Karl Kunisch Pdf

Lagrange multiplier theory provides a tool for the analysis of a general class of nonlinear variational problems and is the basis for developing efficient and powerful iterative methods for solving these problems. This comprehensive monograph analyzes Lagrange multiplier theory and shows its impact on the development of numerical algorithms for problems posed in a function space setting. The authors develop and analyze efficient algorithms for constrained optimization and convex optimization problems based on the augumented Lagrangian concept and cover such topics as sensitivity analysis, convex optimization, second order methods, and shape sensitivity calculus. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black-Scholes model.

Author : Ernesto G. Birgin,Josâ Mario Mart_nez
Publisher : SIAM
Page : 220 pages
File Size : 53,8 Mb
Release : 2014-04-30
Category : Mathematics
ISBN : 9781611973365

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Practical Augmented Lagrangian Methods for Constrained Optimization by Ernesto G. Birgin,Josâ Mario Mart_nez 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; 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 fully describe a freely available computational package for constrained optimization and illustrate its usefulness with applications.

Author : Boris N. Pshenichnyj
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642579189

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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 : Gordon Raymond Walsh
Publisher : John Wiley & Sons
Page : 218 pages
File Size : 55,8 Mb
Release : 1975
Category : Mathematics
ISBN : UOM:39015049377487

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Methods of Optimization by Gordon Raymond Walsh Pdf

Nonlinear programming; Search methods for unconstrained optimization; Gradient methods for unconstrained optimziation; Constrained optimization; Dynamic programming.

Author : Alexander M. Rubinov,Xiao-qi Yang
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 54,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781441991720

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Lagrange-type Functions in Constrained Non-Convex Optimization by Alexander M. Rubinov,Xiao-qi Yang Pdf

Lagrange and penalty function methods provide a powerful approach, both as a theoretical tool and a computational vehicle, for the study of constrained optimization problems. However, for a nonconvex constrained optimization problem, the classical Lagrange primal-dual method may fail to find a mini mum as a zero duality gap is not always guaranteed. A large penalty parameter is, in general, required for classical quadratic penalty functions in order that minima of penalty problems are a good approximation to those of the original constrained optimization problems. It is well-known that penaity functions with too large parameters cause an obstacle for numerical implementation. Thus the question arises how to generalize classical Lagrange and penalty functions, in order to obtain an appropriate scheme for reducing constrained optimiza tion problems to unconstrained ones that will be suitable for sufficiently broad classes of optimization problems from both the theoretical and computational viewpoints. Some approaches for such a scheme are studied in this book. One of them is as follows: an unconstrained problem is constructed, where the objective function is a convolution of the objective and constraint functions of the original problem. While a linear convolution leads to a classical Lagrange function, different kinds of nonlinear convolutions lead to interesting generalizations. We shall call functions that appear as a convolution of the objective function and the constraint functions, Lagrange-type functions.

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 : 51,5 Mb
Release : 1974
Category : Mathematics
ISBN : UOM:39015017289094

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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 : Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher : Unknown
Page : 36 pages
File Size : 54,6 Mb
Release : 1980
Category : Electronic
ISBN : STANFORD:36105046362005

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Computation of the Search Direction in Constrained Optimization Algorithms by Stanford University. Department of Operations Research. Systems Optimization Laboratory Pdf

Author : Andreas Antoniou,Wu-Sheng Lu
Publisher : Springer Science & Business Media
Page : 675 pages
File Size : 44,8 Mb
Release : 2007-03-12
Category : Computers
ISBN : 9780387711065

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Practical Optimization by Andreas Antoniou,Wu-Sheng Lu Pdf

Practical Optimization: Algorithms and Engineering Applications is a hands-on treatment of the subject of optimization. A comprehensive set of problems and exercises makes the book suitable for use in one or two semesters of a first-year graduate course or an advanced undergraduate course. Each half of the book contains a full semester’s worth of complementary yet stand-alone material. The practical orientation of the topics chosen and a wealth of useful examples also make the book suitable for practitioners in the field.

Author : Stephen P. Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 52,9 Mb
Release : 2004-03-08
Category : Business & Economics
ISBN : 0521833787

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Convex Optimization by Stephen P. Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Author : Stanford University. Systems Optimization Laboratory
Publisher : Unknown
Page : 48 pages
File Size : 49,6 Mb
Release : 1979
Category : Electronic
ISBN : STANFORD:36105046361965

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Algorithms for Nonlinearly Constrained Optimization by Stanford University. Systems Optimization Laboratory Pdf

Author : Margaret Ann Hagen Wright
Publisher : Unknown
Page : 554 pages
File Size : 48,6 Mb
Release : 1976
Category : Algorithms
ISBN : STANFORD:36105025663050

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Numerical Methods for Nonlinearly Constrained Optimization by Margaret Ann Hagen Wright Pdf

Author : Dimitri Bertsekas
Publisher : Athena Scientific
Page : 576 pages
File Size : 41,6 Mb
Release : 2015-02-01
Category : Mathematics
ISBN : 9781886529281

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Convex Optimization Algorithms by Dimitri Bertsekas Pdf

This book provides a comprehensive and accessible presentation of algorithms for solving convex optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. This is facilitated by the extensive use of analytical and algorithmic concepts of duality, which by nature lend themselves to geometrical interpretation. The book places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book is aimed at students, researchers, and practitioners, roughly at the first year graduate level. It is similar in style to the author's 2009"Convex Optimization Theory" book, but can be read independently. The latter book focuses on convexity theory and optimization duality, while the present book focuses on algorithmic issues. The two books share notation, and together cover the entire finite-dimensional convex optimization methodology. To facilitate readability, the statements of definitions and results of the "theory book" are reproduced without proofs in Appendix B.

Author : Ernesto G. Birgin,JosŸ Mario Martinez
Publisher : SIAM
Page : 222 pages
File Size : 43,8 Mb
Release : 2014-04-30
Category : Mathematics
ISBN : 9781611973358

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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 : Jorge Nocedal,Stephen Wright
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 51,5 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387227429

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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.