A Family of Hybrid Conjugate Gradient Method with Restart Procedure for Unconstrained Optimizations and Image Restorations PDF Download
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Author: Xianzhen Jiang
Publisher:
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Languages : en
Pages : 0
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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: 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: Ibrahim Jusoh
Publisher:
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Category :
Languages : en
Pages :
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Author: Martin Hanke
Publisher: Routledge
ISBN: 1351458329
Category : Mathematics
Languages : en
Pages : 148
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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: M. J. D. Powell
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 24
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Author: Joseph W. Fischbach
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : en
Pages : 30
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Author: Anand Ramasubramaniam
Publisher:
ISBN:
Category :
Languages : en
Pages : 136
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Author: Donghun Suh
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : en
Pages : 176
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Author: Dianne Prost O'Leary
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 248
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Author: Snezana S. Djordjevic
Publisher:
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Category : Electronic books
Languages : en
Pages : 0
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Here, we consider two important classes of unconstrained optimization methods: conjugate gradient methods and trust region methods. These two classes of methods are very interesting; it seems that they are never out of date. First, we consider conjugate gradient methods. We also illustrate the practical behavior of some conjugate gradient methods. Then, we study trust region methods. Considering these two classes of methods, we analyze some recent results.
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Languages : en
Pages : 0
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