Practical Augmented Lagrangian Methods For Constrained Optimization
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Practical Augmented Lagrangian Methods For Constrained Optimization
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Author : Ernesto G. Birgin
language : en
Publisher: SIAM
Release Date : 2014-04-30
Practical Augmented Lagrangian Methods For Constrained Optimization written by Ernesto G. Birgin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-30 with Mathematics categories.
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.
Practical Augmented Lagrangian Methods For Constrained Optimization
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Author : Ernesto G. Birgin
language : en
Publisher: SIAM
Release Date : 2014-04-30
Practical Augmented Lagrangian Methods For Constrained Optimization written by Ernesto G. Birgin and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-30 with Mathematics categories.
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.
Practical Optimization
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Author : Philip E. Gill
language : en
Publisher:
Release Date : 1981
Practical 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 1981 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
A Globally Convergent Augmented Lagrangian Pattern Search Algorithm For Optimization With General Constraints And Simple Bounds
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Author : Robert Michael Lewis
language : en
Publisher:
Release Date : 1998
A Globally Convergent Augmented Lagrangian Pattern Search Algorithm For Optimization With General Constraints And Simple Bounds written by Robert Michael Lewis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Augmented Lagrangian And Operator Splitting Methods In Nonlinear Mechanics
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Author : Roland Glowinski
language : en
Publisher: SIAM
Release Date : 1989-01-01
Augmented Lagrangian And Operator Splitting Methods In Nonlinear Mechanics written by Roland Glowinski and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Science categories.
This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods.
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.
Augmented Lagrangian Methods
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Author : M. Fortin
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Augmented Lagrangian Methods written by M. Fortin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Mathematics categories.
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.
Global Convergence Of Augmented Lagrangian Methods Applied To Optimization Problems With Degenerate Constraints Including Problems With Complementarity Constraints
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Author : A. F. Izmailov
language : en
Publisher:
Release Date : 2011
Global Convergence Of Augmented Lagrangian Methods Applied To Optimization Problems With Degenerate Constraints Including Problems With Complementarity Constraints written by A. F. Izmailov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
We consider global convergence properties of the augmented Lagrangian methods on problems with degenerate constraints, with a special emphasis on mathematical programs with complementarity constraints (MPCC). In the general case, we show convergence to stationary points of the problem under an error bound condition for the feasible set (which is weaker than constraint qualifications), assuming that the iterates have some modest features of approximate local minimizers of the augmented Lagrangian. For MPCC, we first argue that even weak forms of general constraint qualifications that are suitable for convergence of the augmented Lagrangian methods, such as the recently proposed relaxed positive linear dependence condition, should not be expected to hold and thus special analysis is needed. We next obtain a rather complete picture, showing that under the usual in this context MPCC-linear independence constraint qualification feasible accumulation points of the iterates are guaranteed to be C-stationary for MPCC (better than weakly stationary), but in general need not be M-stationary (hence, neither strongly stationary). However, strong stationarity is guaranteed if the generated dual sequence is bounded, which we show to be the typical numerical behaviour even though the multiplier set itself is unbounded. Experiments with the ALGENCAN augmented Lagrangian solver on the MacMPEC and DEGEN collections are reported, with comparisons to the SNOPT and filterSQP implementations of the SQP method, to the MINOS implementation of the linearly constrained Lagrangian method, and to the interior-point solvers IPOPT and KNITRO. We show that ALGENCAN is a very good option if one is primarily interested in robustness and quality of computed solutions.
Adaptive Augmented Lagrangian Methods
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Author :
language : en
Publisher:
Release Date : 2014
Adaptive Augmented Lagrangian Methods written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Non Smooth And Complementarity Based Distributed Parameter Systems
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Author : Michael Hintermüller
language : en
Publisher: Springer Nature
Release Date : 2022-02-18
Non Smooth And Complementarity Based Distributed Parameter Systems written by Michael Hintermüller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-18 with Mathematics categories.
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.
