Constrained Optimization And Lagrange Multiplier Methods

Author : Dimitri P. Bertsekas
Publisher : Academic Press
ISBN 13 : 148326047X
Total Pages : 412 pages
Book Rating : 4.71/5 ( download)

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Download or read book Constrained Optimization and Lagrange Multiplier Methods written by Dimitri P. Bertsekas and published by Academic Press. This book was released on 2014-05-10 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Dimitri P. Bertsekas
Publisher :
ISBN 13 :
Total Pages : 412 pages
Book Rating : 4.33/5 ( download)

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Download or read book Constrained Optimization and Lagrange Multiplier Methods written by Dimitri P. Bertsekas and published by . This book was released on 1996 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Dimitri P. Bertsekas
Publisher :
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.65/5 ( download)

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Download or read book Constrained Optimization and Lagrange Multiplier Methods written by Dimitri P. Bertsekas and published by . This book was released on 1982 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constrained Optimization and Lagrange Multiplier Methods.

Author : Kazufumi Ito
Publisher : SIAM
ISBN 13 : 0898716497
Total Pages : 354 pages
Book Rating : 4.98/5 ( download)

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Download or read book Lagrange Multiplier Approach to Variational Problems and Applications written by Kazufumi Ito and published by SIAM. This book was released on 2008-11-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.

Author : Kazufumi Ito
Publisher : SIAM
ISBN 13 : 9780898718614
Total Pages : 359 pages
Book Rating : 4.19/5 ( download)

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Download or read book Lagrange Multiplier Approach to Variational Problems and Applications written by Kazufumi Ito and published by SIAM. This book was released on 2008-01-01 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : SIAM
ISBN 13 : 1611973368
Total Pages : 222 pages
Book Rating : 4.65/5 ( download)

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Download or read book Practical Augmented Lagrangian Methods for Constrained Optimization written by Ernesto G. Birgin and published by SIAM. This book was released on 2014-04-30 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.87/5 ( download)

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Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Boris N. Pshenichnyj
Publisher : Springer Science & Business Media
ISBN 13 : 3642579183
Total Pages : 156 pages
Book Rating : 4.89/5 ( download)

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Download or read book The Linearization Method for Constrained Optimization written by Boris N. Pshenichnyj and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Andreas Antoniou
Publisher : Springer Science & Business Media
ISBN 13 : 0387711066
Total Pages : 675 pages
Book Rating : 4.65/5 ( download)

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Download or read book Practical Optimization written by Andreas Antoniou and published by Springer Science & Business Media. This book was released on 2007-03-12 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alexander M. Rubinov
Publisher : Springer Science & Business Media
ISBN 13 : 1441991727
Total Pages : 297 pages
Book Rating : 4.20/5 ( download)

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Download or read book Lagrange-type Functions in Constrained Non-Convex Optimization written by Alexander M. Rubinov and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.