Mathematical Programming Via Augmented Lagrangians PDF Download

Author: Donald A. Pierre
Publisher: Addison Wesley Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 470

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Book Description

Author: Roland Glowinski
Publisher: SIAM
ISBN: 0898712300
Category : Science
Languages : en
Pages : 301

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Book Description
This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods.

Author: M. Fortin
Publisher: Elsevier
ISBN: 008087536X
Category : Mathematics
Languages : en
Pages : 361

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Book Description
The purpose of this volume is to present the principles of the Augmented Lagrangian Method, together with numerous applications of this method to the numerical solution of boundary-value problems for partial differential equations or inequalities arising in Mathematical Physics, in the Mechanics of Continuous Media and in the Engineering Sciences.

Author: Stephen Boyd
Publisher: Now Publishers Inc
ISBN: 160198460X
Category : Computers
Languages : en
Pages : 138

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Book Description
Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.

Author: Ernesto G. Birgin
Publisher: SIAM
ISBN: 161197335X
Category : Mathematics
Languages : en
Pages : 222

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Book Description
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: J. P. Ponstein
Publisher: Cambridge University Press
ISBN: 9780521604918
Category : Mathematics
Languages : en
Pages : 224

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Book Description
A concise account which finds the optimal solution to mathematical problems arising in economics, engineering, the social and mathematical sciences.

Author: Antonio J. Conejo
Publisher: Springer Science & Business Media
ISBN: 3540276866
Category : Technology & Engineering
Languages : en
Pages : 542

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Book Description
Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.

Author: Dimitri P. Bertsekas
Publisher: Academic Press
ISBN: 148326047X
Category : Mathematics
Languages : en
Pages : 412

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Book Description
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:
Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 1038

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Book Description

Author: Jean-Baptiste Hiriart-Urruty
Publisher: Springer Science & Business Media
ISBN: 3662027968
Category : Mathematics
Languages : en
Pages : 432

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Book Description
Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.