Practical Augmented Lagrangian Methods For Constrained Optimization

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.

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. 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.

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.

Download or read book Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics written by Roland Glowinski and published by SIAM. This book was released on 1989-01-01 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods.

Download or read book Practical Optimization written by Philip E. Gill and published by SIAM. This book was released on 2019-12-16 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the intervening years since this book was published in 1981, the field of optimization has been exceptionally lively. This fertility has involved not only progress in theory, but also faster numerical algorithms and extensions into unexpected or previously unknown areas such as semidefinite programming. Despite these changes, many of the important principles and much of the intuition can be found in this Classics version of Practical Optimization. This book provides model algorithms and pseudocode, useful tools for users who prefer to write their own code as well as for those who want to understand externally provided code. It presents algorithms in a step-by-step format, revealing the overall structure of the underlying procedures and thereby allowing a high-level perspective on the fundamental differences. And it contains a wealth of techniques and strategies that are well suited for optimization in the twenty-first century, and particularly in the now-flourishing fields of data science, “big data,” and machine learning. Practical Optimization is appropriate for advanced undergraduates, graduate students, and researchers interested in methods for solving optimization problems.

Download or read book Non-Smooth and Complementarity-Based Distributed Parameter Systems written by Michael Hintermüller and published by Springer Nature. This book was released on 2022-02-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

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.