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Preconditioning Methods For Linear Systems Arising In Constrained Optimization Problems
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Book Synopsis Preconditioning Methods for Linear Systems Arising in Constrained Optimization Problems by : A. Owe H. Axelsson
Download or read book Preconditioning Methods for Linear Systems Arising in Constrained Optimization Problems written by A. Owe H. Axelsson and published by . This book was released on 2002 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Elements and Fast Iterative Solvers by : Howard Elman
Download or read book Finite Elements and Fast Iterative Solvers written by Howard Elman and published by OUP Oxford. This book was released on 2014-06-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
Book Synopsis Iterative Solution Methods by : Owe Axelsson
Download or read book Iterative Solution Methods written by Owe Axelsson and published by Cambridge University Press. This book was released on 1996-03-29 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals primarily with the numerical solution of linear systems of equations by iterative methods. The first part of the book is intended to serve as a textbook for a numerical linear algebra course. The material assumes the reader has a basic knowledge of linear algebra, such as set theory and matrix algebra, however it is demanding for students who are not afraid of theory. To assist the reader, the more difficult passages have been marked, the definitions for each chapter are collected at the beginning of the chapter, and numerous exercises are included throughout the text. The second part of the book serves as a monograph introducing recent results in the iterative solution of linear systems, mainly using preconditioned conjugate gradient methods. This book should be a valuable resource for students and researchers alike wishing to learn more about iterative methods.
Book Synopsis Preconditioning a Product of Matrices Arising in Trust Region Subproblems by :
Download or read book Preconditioning a Product of Matrices Arising in Trust Region Subproblems written by and published by . This book was released on 1996 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In solving large scale optimization problems, we find it advantageous to use iterative methods to solve the sparse linear systems that arise. In the ETR software for solving equality constrained optimization problems, we use a conjugate gradient method to approximately solve the trust region subproblems. To speed up the convergence of the conjugate gradient routine, we need to precondition matrices of the form Z{sup T} W Z, which are not explicitly stored. Four preconditioners were implemented and the results for each are given.
Book Synopsis Perconditioning Methods for Linear Systems Arising in Constrained Optimization Problems by : Owe Axelsson
Download or read book Perconditioning Methods for Linear Systems Arising in Constrained Optimization Problems written by Owe Axelsson and published by . This book was released on 2002 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad
Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.
Book Synopsis Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs by : Josef Malek
Download or read book Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs written by Josef Malek and published by SIAM. This book was released on 2014-12-22 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?
Book Synopsis Preconditioning Methods for Constrained Optimization Problems with Applications for the Linear Elasticity Equations by : A. Owe H. Axelsson
Download or read book Preconditioning Methods for Constrained Optimization Problems with Applications for the Linear Elasticity Equations written by A. Owe H. Axelsson and published by . This book was released on 2003 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by : Daniele Bertaccini
Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Book Synopsis The Linearization Method for Constrained Optimization by : Boris N. Pshenichnyj
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 :Wilhelmus H. Schilders Publisher :Springer Science & Business Media ISBN 13 :3540788417 Total Pages :471 pages Book Rating :4.5/5 (47 download)
Book Synopsis Model Order Reduction: Theory, Research Aspects and Applications by : Wilhelmus H. Schilders
Download or read book Model Order Reduction: Theory, Research Aspects and Applications written by Wilhelmus H. Schilders and published by Springer Science & Business Media. This book was released on 2008-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
Book Synopsis Acta Numerica 2005: Volume 14 by : Arieh Iserles
Download or read book Acta Numerica 2005: Volume 14 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2005-06-30 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.
Book Synopsis Large-Scale Scientific Computing by : Ivan Lirkov
Download or read book Large-Scale Scientific Computing written by Ivan Lirkov and published by Springer. This book was released on 2020-02-14 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes revised papers from the 12th International Conference on Large-Scale Scientific Computing, LSSC 2019, held in Sozopol, Bulgaria, in June 2019. The 70 papers presented in this volume were carefully reviewed and selected from 81 submissions. The book also contains two invited talks. The papers were organized in topical sections named as follows: control and optimization of dynamical systems; meshfree and particle methods; fractional diffusion problems: numerical methods, algorithms and applications; pore scale flow and transport simulation; tensors based algorithms and structures in optimization and applications; HPC and big data: algorithms and applications; large-scale models: numerical methods, parallel computations and applications; monte carlo algorithms: innovative applications in conjunctions with other methods; application of metaheuristics to large-scale problems; large scale machine learning: multiscale algorithms and performance guarantees; and contributed papers.
Book Synopsis Real-time PDE-constrained Optimization by : Lorenz T. Biegler
Download or read book Real-time PDE-constrained Optimization written by Lorenz T. Biegler and published by SIAM. This book was released on 2007-01-01 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.
Book Synopsis Numerical Methods and Applications by : Ivan Lirkov
Download or read book Numerical Methods and Applications written by Ivan Lirkov and published by Springer Science & Business Media. This book was released on 2003 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods for PDE-constrained Optimization by : Joseph Robert Reed
Download or read book Methods for PDE-constrained Optimization written by Joseph Robert Reed and published by . This book was released on 2011 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: The KKT systems arising in nonlinearly constrained optimization problems may not have correct inertia, and therefore must be modified to avoid convergence to nonoptimal KKT points. Matrix factorizations can determine the inertia of a general symmetric matrix but are too costly in the PDE contextIn PDE-constrained optimization, KKT systems are generally solved with preconditioned iterative methods that are unable to detect whether the current matrix has correct inertia. Moreover, the preconditioners assume the existence of a preconditioner for the underlying PDE. Methods are discussed that solve the constrained problem by minimizing a sequence of smooth primal-dual merit functions. The Newton equations are solved approximately with a variant of the preconditioned conjugate-gradient (PCG) method that naturally determines when the regularized KKT system for the constrained problem has incorrect inertia. Convergence is accelerated with a sparsity exploiting preconditioner that implicitly defines a positive-definite system. The preconditioning strategy is entirely algebraic and is based on an incomplete factorization of an equivalent symmetric indefinite system. It explicitly takes advantage of dual regularization, and in the PDE constrained context, does not require a preconditioner for the underlying PDE.
Book Synopsis Topics in Optimization and Sparse Linear Systems by : Anil Joshi
Download or read book Topics in Optimization and Sparse Linear Systems written by Anil Joshi and published by . This book was released on 1996 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "In the first part of the thesis, we study three problems in optimization -- Network Optimization Problem, A Convex Optimization Problem arising out of Timing Analysis of VLSI circuits, and A Geometric Solution to two variable Convex Optimization Problems. In the second part of the thesis, we analyze the quality of a new graph-based preconditioner for large sparse Symmetric Positive Definite Diagonally Dominant (SPDDD) linear systems. These kinds of linear systems arise in the solution of scalar second order PDEs for Heat Transfer, Electrostatics, Electromagnetics, Ground Water Flow, and Diffusion (with or without reaction) when they are discretized using finite differences. They also arise in discrete problems like Network Flow Problems (Assignment, Maximum Flow, and Minimum Cost Flow), Large Resistive Networks, and Laminar Flow in Pipe Networks."
