A New Family of Conjugate Gradient Methods for Large-scale Unconstrained Optimization PDF Download
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Author: Ibrahim Jusoh
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Ibrahim Jusoh
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Neculai Andrei
Publisher: Springer Nature
ISBN: 3030429504
Category : Mathematics
Languages : en
Pages : 515
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Book Description
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: Radoslaw Pytlak
Publisher: Springer Science & Business Media
ISBN: 354085634X
Category : Mathematics
Languages : en
Pages : 493
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Book Description
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: Xianzhen Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Conjugate gradient method is one of the most effective methods for solving large-scale optimization problems. Based on the CD conjugate parameter and an improved PRP conjugate parameter,a modified conjugate gradient method with a single-parameter can be designed. To improve its convergence property and computational efficiency, this conjugate parameter is further improved by using the hybrid technique in its denominator, and meanwhile a restart procedure is set in its search direction. Accordingly, a family of hybrid conjugate gradient method with restart procedure is established in this paper, which is sufficient descent at each iteration without depending onany selection of line search criterions. Under usual assumptions and using the weak Wolfe line search criterion to generate the steplengths, the global convergence of the proposed family is proved.Finally, choosing a specific algorithm from this family to solve large-scale unconstrained optimization problems and image restoration, all the numerical results show that the new algorithm is effective.
Author: Philip Wolfe
Publisher:
ISBN:
Category : Programming (Mathematics).
Languages : en
Pages : 564
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Book Description
A NATO Summer School held in Bandol, France, sponsored by the Scientific Affairs Division of NATO.
Author: Amal Ahmed Al-Saidiyah
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 0387747583
Category : Mathematics
Languages : en
Pages : 4646
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Book Description
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: Mary Catherine Fenelon
Publisher:
ISBN:
Category : Large scale systems
Languages : en
Pages : 288
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Book Description
Author: Martin Hanke
Publisher: Routledge
ISBN: 1351458329
Category : Mathematics
Languages : en
Pages : 148
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Book Description
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: Masao Fukushima
Publisher: Springer Science & Business Media
ISBN: 9780792353201
Category : Mathematics
Languages : en
Pages : 468
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Book Description
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.
