Augmented Lagrangian Methods

Author : Ernesto G. Birgin,JosŸ Mario Martinez
Publisher : SIAM
Page : 222 pages
File Size : 43,7 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 : Ernesto G. Birgin,Josâ Mario Mart_nez
Publisher : SIAM
Page : 220 pages
File Size : 49,7 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 : M. Fortin,R. Glowinski
Publisher : Elsevier
Page : 339 pages
File Size : 51,5 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 008087536X

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Augmented Lagrangian Methods by M. Fortin,R. Glowinski Pdf

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 : Roland Glowinski,Patrick Le Tallec
Publisher : SIAM
Page : 301 pages
File Size : 45,7 Mb
Release : 1989-01-01
Category : Science
ISBN : 9780898712308

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Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics by Roland Glowinski,Patrick Le Tallec Pdf

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

Author : Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie
Publisher : Springer Science & Business Media
Page : 882 pages
File Size : 43,6 Mb
Release : 2009-05-25
Category : Computers
ISBN : 9783642022555

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Scale Space and Variational Methods in Computer Vision by Xue-Cheng Tai,Knut Morken,Marius Lysaker,Knut-Andreas Lie Pdf

This book constitutes the refereed proceedings of the Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, emanated from the joint edition of the 5th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2009 and the 7th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2009, held in Voss, Norway in June 2009. The 71 revised full papers presented were carefully reviewed and selected numerous submissions. The papers are organized in topical sections on segmentation and detection; image enhancement and reconstruction; motion analysis, optical flow, registration and tracking; surfaces and shapes; scale space and feature extraction.

Author : Dimitri P. Bertsekas
Publisher : Academic Press
Page : 412 pages
File Size : 53,7 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 : 354 pages
File Size : 54,9 Mb
Release : 2008-11-06
Category : Mathematics
ISBN : 9780898716498

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

Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.

Author : Jonas Siegfried Jehle
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2018
Category : Electronic
ISBN : OCLC:1187594536

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First-order Augmented Lagrangian Methods for State Constraint Problems by Jonas Siegfried Jehle Pdf

Author : Stephen Boyd,Neal Parikh,Eric Chu
Publisher : Now Publishers Inc
Page : 138 pages
File Size : 42,9 Mb
Release : 2011
Category : Computers
ISBN : 9781601984609

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Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers by Stephen Boyd,Neal Parikh,Eric Chu Pdf

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 : Ronald Glowinski,Patrick Le Tallec
Publisher : SIAM
Page : 300 pages
File Size : 40,7 Mb
Release : 1989-01-01
Category : Science
ISBN : 1611970830

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Augmented Lagrangian and Operator-splitting Methods in Nonlinear Mechanics by Ronald Glowinski,Patrick Le Tallec Pdf

A need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator-splitting methods such as alternating-methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite-element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods additionally used to study them. These ideas are then applied to specific classes of mechanical problems.

Author : Neculai Andrei
Publisher : Springer
Page : 506 pages
File Size : 48,8 Mb
Release : 2017-12-04
Category : Mathematics
ISBN : 9783319583563

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Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology by Neculai Andrei Pdf

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.

Author : Anthony V. Fiacco,Garth P. McCormick
Publisher : SIAM
Page : 224 pages
File Size : 45,8 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 9780898712544

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Nonlinear Programming by Anthony V. Fiacco,Garth P. McCormick Pdf

Analyzes the 'central' or 'dual' trajectory used by modern path following and primal/dual methods for convex / general linear programming.

Author : Michael Stingl
Publisher : Unknown
Page : 150 pages
File Size : 52,7 Mb
Release : 2006
Category : Nonlinear programming
ISBN : 3832253335

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On the Solution of Nonlinear Semidefinite Programs by Augmented Lagrangian Methods by Michael Stingl Pdf

Author : Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio
Publisher : Springer Nature
Page : 316 pages
File Size : 44,6 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : 9783030598372

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Mean Field Games by Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio Pdf

This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.

Author : Robert Michael Lewis,Institute for Computer Applications in Science and Engineering,Virginia Torczon
Publisher : Unknown
Page : 22 pages
File Size : 50,7 Mb
Release : 1998
Category : Electronic
ISBN : NASA:31769000708084

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A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds by Robert Michael Lewis,Institute for Computer Applications in Science and Engineering,Virginia Torczon Pdf