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Author : Loyce M. Adams,John Lawrence Nazareth
Publisher : SIAM
Page : 186 pages
File Size : 55,5 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0898713765
Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.
Author : Neculai Andrei
Publisher : Springer Nature
Page : 515 pages
File Size : 52,5 Mb
Release : 2020-06-23
Category : Mathematics
ISBN : 9783030429508
Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.
Author : Neculai Andrei
Publisher : Springer
Page : 486 pages
File Size : 42,6 Mb
Release : 2020-06-29
Category : Mathematics
ISBN : 3030429490
Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.
Author : Michal Krizek,Pekka Neittaanmäki,Roland Glowinski,Sergey Korotov
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642185601
The position taken in this collection of pedagogically written essays is that conjugate gradient algorithms and finite element methods complement each other extremely well. Via their combinations practitioners have been able to solve complicated, direct and inverse, multidemensional problems modeled by ordinary or partial differential equations and inequalities, not necessarily linear, optimal control and optimal design being part of these problems. The aim of this book is to present both methods in the context of complicated problems modeled by linear and nonlinear partial differential equations, to provide an in-depth discussion on their implementation aspects. The authors show that conjugate gradient methods and finite element methods apply to the solution of real-life problems. They address graduate students as well as experts in scientific computing.
Author : James W. Daniel
Publisher : Unknown
Page : 198 pages
File Size : 55,8 Mb
Release : 1965
Category : Equations
ISBN : STANFORD:36105010198682
Author : William L. Briggs,Van Emden Henson,Steve F. McCormick
Publisher : SIAM
Page : 318 pages
File Size : 46,6 Mb
Release : 2000-07-01
Category : Mathematics
ISBN : 0898714621
Mathematics of Computing -- Numerical Analysis.
Author : Gérard Meurant ,Petr Tichý
Publisher : SIAM
Page : 138 pages
File Size : 47,6 Mb
Release : 2024-01-30
Category : Mathematics
ISBN : 9781611977868
The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.
Author : Radoslaw Pytlak
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 52,6 Mb
Release : 2008-11-18
Category : Mathematics
ISBN : 9783540856344
This book details algorithms for large-scale unconstrained and bound constrained optimization. It shows optimization techniques from a conjugate gradient algorithm perspective as well as methods of shortest residuals, which have been developed by the author.
Author : Ya-xiang Yuan
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 46,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461333357
About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by M. H. Wright (SIAM President, Bell Labs), "Interior point trajectories in semidefinite programming" by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe matical Programming), "An approach to derivative free optimization" by A.
Author : Mary Catherine Hill
Publisher : Unknown
Page : 54 pages
File Size : 50,6 Mb
Release : 1990
Category : Groundwater
ISBN : UIUC:30112098737692
Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 50,5 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Author : Martin Hanke
Publisher : Routledge
Page : 115 pages
File Size : 42,5 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351458320
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
Author : Igor Griva,Stephen G. Nash,Ariela Sofer
Publisher : SIAM
Page : 743 pages
File Size : 50,5 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898717730
Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.
Author : Masao Fukushima,Liqun Qi
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 52,6 Mb
Release : 1999
Category : Mathematics
ISBN : 079235320X
The concept of `reformulation' has long played an important role in mathematical programming. A classical example is the penalization technique in constrained optimization. More recent trends consist of reformulation of various mathematical programming problems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. The book is a collection of peer-reviewed papers that cover such diverse areas as linear and nonlinear complementarity problems, variational inequality problems, nonsmooth equations and nonsmooth optimization problems, economic and network equilibrium problems, semidefinite programming problems, maximal monotone operator problems, and mathematical programs with equilibrium constraints. The reader will be convinced that the concept of `reformulation' provides extremely useful tools for advancing the study of mathematical programming from both theoretical and practical aspects. Audience: This book is intended for students and researchers in optimization, mathematical programming, and operations research.
Author : Mordecai Avriel
Publisher : Courier Corporation
Page : 548 pages
File Size : 40,8 Mb
Release : 2003-01-01
Category : Mathematics
ISBN : 0486432270
This overview provides a single-volume treatment of key algorithms and theories. Begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs, and then explores techniques for numerical solutions and unconstrained optimization methods. 1976 edition. Includes 58 figures and 7 tables.
