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Download or read book Adaptive Augmented Lagrangian Methods written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wenda Zhang
Publisher :
ISBN 13 : 9781303915529
Total Pages : 42 pages
Book Rating : 4.9/5 (155 download)
Download or read book A Subproblem Algorithm for the Adaptive Augmented Lagrangian Method written by Wenda Zhang and published by . This book was released on 2014 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: An adaptive augmented Lagrangian algorithm is presented to overcome some undesirable behavior of traditional augmented Lagrangian methods. While the method has previously been proposed in \cite{AAL}, the goal in this thesis is to improve its practical performance. In particular, we propose an active set projected conjugate gradient (ASPCG) method for solving the subproblems of the adaptive augmented Lagrangian algorithm. The proposed ASPCG algorithm first estimates the optimal active set and then performs a projected conjugate gradient method to produce the exact or at least a good approximate solution updating the active set estimate when appropriate. We perform a series of numerical experiments to determine if the proposed algorithm is superior in some critical performance measures to the solver originally implemented in the adaptive augmented Lagrangian algorithm. In addition, we conduct experiments to monitor the performance of the adaptive augmented Lagrangian algorithm when some of its key features are modified.
Author : Ernesto G. Birgin
Publisher : SIAM
ISBN 13 : 1611973368
Total Pages : 222 pages
Book Rating : 4.6/5 (119 download)
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 : M. Fortin
Publisher : Elsevier
ISBN 13 : 008087536X
Total Pages : 361 pages
Book Rating : 4.0/5 (88 download)
Download or read book Augmented Lagrangian Methods written by M. Fortin and published by Elsevier. This book was released on 2000-04-01 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : SIAM
ISBN 13 : 0898712300
Total Pages : 301 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Robert Michael Lewis
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (317 download)
Download or read book A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds written by Robert Michael Lewis and published by . This book was released on 1998 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Veronika Karl
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (122 download)
Download or read book Augmented Lagrangian Methods for State Constrained Optimal Control Problems written by Veronika Karl and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529310
Total Pages : 256 pages
Book Rating : 4.8/5 (865 download)
Download or read book Convex Optimization Theory written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2009-06-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).
Author : Stéphane Vincent
Publisher : Springer Nature
ISBN 13 : 3031092651
Total Pages : 314 pages
Book Rating : 4.0/5 (31 download)
Download or read book Small Scale Modeling and Simulation of Incompressible Turbulent Multi-Phase Flow written by Stéphane Vincent and published by Springer Nature. This book was released on 2022-10-06 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides basic and recent research insights concerning the small scale modeling and simulation of turbulent multi-phase flows. By small scale, it has to be understood that the grid size for the simulation is smaller than most of the physical time and space scales of the problem. Small scale modeling of multi-phase flows is a very popular topic since the capabilities of massively parallel computers allows to go deeper into the comprehension and characterization of realistic flow configurations and at the same time, many environmental and industrial applications are concerned such as nuclear industry, material processing, chemical reactors, engine design, ocean dynamics, pollution and erosion in rivers or on beaches. The work proposes a complete and exhaustive presentation of models and numerical methods devoted to small scale simulation of incompressible turbulent multi-phase flows from specialists of the research community. Attention has also been paid to promote illustrations and applications, multi-phase flows and collaborations with industry. The idea is also to bring together developers and users of different numerical approaches and codes to share their experience in the development and validation of the algorithms and discuss the difficulties and limitations of the different methods and their pros and cons. The focus will be mainly on fixed-grid methods, however adaptive grids will be also partly broached, with the aim to compare and validate the different approaches and models.
Author : Zdenek Dostál
Publisher : Springer Science & Business Media
ISBN 13 : 0387848061
Total Pages : 293 pages
Book Rating : 4.3/5 (878 download)
Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.
Author : Asma Atamna
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (987 download)
Download or read book Analysis of Randomized Adaptive Algorithms for Black-Box Continuous Constrained Optimization written by Asma Atamna and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate various aspects of adaptive randomized (or stochastic) algorithms for both constrained and unconstrained black-box continuous optimization. The first part of this thesis focuses on step-size adaptation in unconstrained optimization. We first present a methodology for assessing efficiently a step-size adaptation mechanism that consists in testing a given algorithm on a minimal set of functions, each reflecting a particular difficulty that an efficient step-size adaptation algorithm should overcome. We then benchmark two step-size adaptation mechanisms on the well-known BBOB noiseless testbed and compare their performance to the one of the state-of-the-art evolution strategy (ES), CMA-ES, with cumulative step-size adaptation. In the second part of this thesis, we investigate linear convergence of a (1 + 1)-ES and a general step-size adaptive randomized algorithm on a linearly constrained optimization problem, where an adaptive augmented Lagrangian approach is used to handle the constraints. To that end, we extend the Markov chain approach used to analyze randomized algorithms for unconstrained optimization to the constrained case. We prove that when the augmented Lagrangian associated to the problem, centered at the optimum and the corresponding Lagrange multipliers, is positive homogeneous of degree 2, then for algorithms enjoying some invariance properties, there exists an underlying homogeneous Markov chain whose stability (typically positivity and Harris-recurrence) leads to linear convergence to both the optimum and the corresponding Lagrange multipliers. We deduce linear convergence under the aforementioned stability assumptions by applying a law of large numbers for Markov chains. We also present a general framework to design an augmented-Lagrangian-based adaptive randomized algorithm for constrained optimization, from an adaptive randomized algorithm for unconstrained optimization.
Author : A. F. Izmailov
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (93 download)
Download or read book Global Convergence of Augmented Lagrangian Methods Applied to Optimization Problems with Degenerate Constraints, Including Problems with Complementarity Constraints written by A. F. Izmailov and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : James A. Momoh
Publisher : CRC Press
ISBN 13 : 1439829799
Total Pages : 443 pages
Book Rating : 4.4/5 (398 download)
Download or read book Adaptive Stochastic Optimization Techniques with Applications written by James A. Momoh and published by CRC Press. This book was released on 2015-12-02 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive Stochastic Optimization Techniques with Applications provides a single, convenient source for state-of-the-art information on optimization techniques used to solve problems with adaptive, dynamic, and stochastic features. Presenting modern advances in static and dynamic optimization, decision analysis, intelligent systems, evolutionary pro
Author : Xiaoxi Jia
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book Augmented Lagrangian Methods Invoking (Proximal) Gradient-type Methods for (Composite) Structured Optimization Problems written by Xiaoxi Jia and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kazufumi Ito
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (755 download)
Download or read book Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces written by Kazufumi Ito and published by . This book was released on 1994 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Weizhang Huang
Publisher : Springer Science & Business Media
ISBN 13 : 1441979166
Total Pages : 446 pages
Book Rating : 4.4/5 (419 download)
Download or read book Adaptive Moving Mesh Methods written by Weizhang Huang and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
Author : Jong-Shi Pang
Publisher : Springer Science & Business Media
ISBN 13 : 1461551978
Total Pages : 266 pages
Book Rating : 4.4/5 (615 download)
Download or read book Computational Optimization written by Jong-Shi Pang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Optimization: A Tribute to Olvi Mangasarian serves as an excellent reference, providing insight into some of the most challenging research issues in the field. This collection of papers covers a wide spectrum of computational optimization topics, representing a blend of familiar nonlinear programming topics and such novel paradigms as semidefinite programming and complementarity-constrained nonlinear programs. Many new results are presented in these papers which are bound to inspire further research and generate new avenues for applications. An informal categorization of the papers includes: Algorithmic advances for special classes of constrained optimization problems Analysis of linear and nonlinear programs Algorithmic advances B- stationary points of mathematical programs with equilibrium constraints Applications of optimization Some mathematical topics Systems of nonlinear equations.
