The Linearization Method For Constrained Optimization
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The Linearization Method For Constrained Optimization
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Author : Boris N. Pshenichnyj
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Linearization Method For Constrained Optimization written by Boris N. Pshenichnyj 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 2012-12-06 with Science categories.
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.
Constrained Optimization And Lagrange Multiplier Methods
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Author : Dimitri P. Bertsekas
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Constrained Optimization And Lagrange Multiplier Methods written by Dimitri P. Bertsekas and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
A Reformulation Linearization Technique For Solving Discrete And Continuous Nonconvex Problems
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Author : Hanif D. Sherali
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Reformulation Linearization Technique For Solving Discrete And Continuous Nonconvex Problems written by Hanif D. Sherali 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 2013-04-17 with Mathematics categories.
This book deals with the theory and applications of the Reformulation- Linearization/Convexification Technique (RL T) for solving nonconvex optimization problems. A unified treatment of discrete and continuous nonconvex programming problems is presented using this approach. In essence, the bridge between these two types of nonconvexities is made via a polynomial representation of discrete constraints. For example, the binariness on a 0-1 variable x . can be equivalently J expressed as the polynomial constraint x . (1-x . ) = 0. The motivation for this book is J J the role of tight linear/convex programming representations or relaxations in solving such discrete and continuous nonconvex programming problems. The principal thrust is to commence with a model that affords a useful representation and structure, and then to further strengthen this representation through automatic reformulation and constraint generation techniques. As mentioned above, the focal point of this book is the development and application of RL T for use as an automatic reformulation procedure, and also, to generate strong valid inequalities. The RLT operates in two phases. In the Reformulation Phase, certain types of additional implied polynomial constraints, that include the aforementioned constraints in the case of binary variables, are appended to the problem. The resulting problem is subsequently linearized, except that certain convex constraints are sometimes retained in XV particular special cases, in the Linearization/Convexijication Phase. This is done via the definition of suitable new variables to replace each distinct variable-product term. The higher dimensional representation yields a linear (or convex) programming relaxation.
Introduction To Optimization Methods
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Author : P. Adby
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Optimization Methods written by P. Adby 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 2013-03-09 with Science categories.
During the last decade the techniques of non-linear optim ization have emerged as an important subject for study and research. The increasingly widespread application of optim ization has been stimulated by the availability of digital computers, and the necessity of using them in the investigation of large systems. This book is an introduction to non-linear methods of optimization and is suitable for undergraduate and post graduate courses in mathematics, the physical and social sciences, and engineering. The first half of the book covers the basic optimization techniques including linear search methods, steepest descent, least squares, and the Newton-Raphson method. These are described in detail, with worked numerical examples, since they form the basis from which advanced methods are derived. Since 1965 advanced methods of unconstrained and constrained optimization have been developed to utilise the computational power of the digital computer. The second half of the book describes fully important algorithms in current use such as variable metric methods for unconstrained problems and penalty function methods for constrained problems. Recent work, much of which has not yet been widely applied, is reviewed and compared with currently popular techniques under a few generic main headings. vi PREFACE Chapter I describes the optimization problem in mathemat ical form and defines the terminology used in the remainder of the book. Chapter 2 is concerned with single variable optimization. The main algorithms of both search and approximation methods are developed in detail since they are an essential part of many multi-variable methods.
An Introduction To Nonlinear Optimization Theory
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Author : Marius Durea
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-01-01
An Introduction To Nonlinear Optimization Theory written by Marius Durea and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-01 with Mathematics categories.
The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization. Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical aspects of this field. This book prepares those who are engaged in research by giving repeated insights into ideas that are subsequently dealt with and illustrated in detail.
Methods Of Optimization
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Author : Gordon Raymond Walsh
language : en
Publisher: John Wiley & Sons
Release Date : 1975
Methods Of Optimization written by Gordon Raymond Walsh and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Nonlinear programming; Search methods for unconstrained optimization; Gradient methods for unconstrained optimziation; Constrained optimization; Dynamic programming.
Constrained Optimization In The Calculus Of Variations And Optimal Control Theory
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Author : J Gregory
language : en
Publisher: CRC Press
Release Date : 2018-01-18
Constrained Optimization In The Calculus Of Variations And Optimal Control Theory written by J Gregory and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.
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.
Practical Methods Of Optimization Constrained Optimization
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Author : Roger Fletcher
language : en
Publisher:
Release Date : 1980
Practical Methods Of Optimization Constrained Optimization written by Roger Fletcher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematical optimization categories.
Numerical Methods For Constrained Optimization
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Author : Philip E. Gill
language : en
Publisher:
Release Date : 1974
Numerical Methods For Constrained Optimization written by Philip E. Gill and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Numerical Optimization
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Author : Jorge Nocedal
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-06
Numerical Optimization written by Jorge Nocedal 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 2006-06-06 with Mathematics categories.
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.