Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line Search

Al-Baali, Mehiddin

doi:10.1093/imanum/5.1.121

Cited by 434 publications

(286 citation statements)

References 4 publications

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“…Therefore s k y (1) k is sufficiently positive for suited values of the parameters σ and η k . Moreover, we can guarantee that y (1) k satisfies (3.17) by setting η k > 1 whenever s k y k > 0.…”

Section: Novel Damped Strategiesmentioning

confidence: 94%

“…We started by considering our first proposal, namely the use of the damped vector y (1) k in (3.12) combined with the adaptive rule in (3.14). First of all, we needed to tune the choice of the two parameters η k in (3.12) and σ in (3.14).…”

Section: Damped Preconditioned Ncg Methods: a Numerical Experiencementioning

confidence: 99%

“…Moreover, we can guarantee that y (1) k satisfies (3.17) by setting η k > 1 whenever s k y k > 0. On the other hand, if s k y k is negative, (3.17) is trivially satisfied by the choice y (1) k . In our second proposal we set z k = −α k g k in (3.12) to obtain the damped vector…”

Section: Novel Damped Strategiesmentioning

confidence: 99%

“…Finally, observe that in our first proposal the conditions (3.14)-(3.18) omit the dependency on any considerations regarding the global convergence of the final damped techniques. In this regard, a further study on the latter issue (see also [1] [2] [8]) seems to be necessary, which will be the object of future research.…”

Section: Novel Damped Strategiesmentioning

confidence: 99%

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Exploiting damped techniques for nonlinear conjugate gradient methods

et al. 2017

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In this paper we propose the use of damped techniques within Nonlinear Conjugate Gradient (NCG) methods. Damped techniques were introduced by Powell and recently reproposed by Al-Baali and till now, only applied in the framework of quasi-Newton methods. We extend their use to NCG methods in large scale unconstrained optimization, aiming at possibly improving the efficiency and the robustness of the latter methods, especially when solving difficult problems. We consider both unpreconditioned and Preconditioned NCG (PNCG). In the latter case, we embed damped techniques within a class of preconditioners based on quasi-Newton updates. Our purpose is to possibly provide efficient preconditioners which approximate, in some sense, the inverse of the Hessian matrix, while still preserving information provided by the secant equation or some of its modifications. The results of an extensive numerical experience highlights that the proposed approach is quite promising.

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Section: Novel Damped Strategiesmentioning

confidence: 94%

Section: Damped Preconditioned Ncg Methods: a Numerical Experiencementioning

confidence: 99%

Section: Novel Damped Strategiesmentioning

confidence: 99%

Section: Novel Damped Strategiesmentioning

confidence: 99%

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Exploiting damped techniques for nonlinear conjugate gradient methods

et al. 2017

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“…When σy T k s k > 0, for any line search, the directions defined by (5) satisfy the descent property [1] d T k+1 g k+1 < 0,…”

Section: Introductionmentioning

confidence: 99%

Symmetric Perry conjugate gradient method

Liu

2013

Comput Optim Appl

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A family of new conjugate gradient methods is proposed based on Perry's idea, which satisfies the descent property or the sufficient descent property for any line search. In addition, based on the scaling technology and the restarting strategy, a family of scaling symmetric Perry conjugate gradient methods with restarting procedures is presented. The memoryless BFGS method and the SCALCG method are the special forms of the two families of new methods, respectively. Moreover, several concrete new algorithms are suggested. Under Wolfe line searches, the global convergence of the two families of the new methods is proven by the spectral analysis for uniformly convex functions and nonconvex functions. The preliminary numerical comparisons with CG_DESCENT and SCALCG algorithms show that these new algorithms are very effective algorithms for the large-scale unconstrained optimization problems. Finally, a remark for further research is suggested.

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Nonlinear Conjugate Gradient Methods

Dai¹

2011

Wiley Encyclopedia of Operations Research and Management Science

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Conjugate gradient methods are a class of important methods for solving linear equations and for solving nonlinear optimization. In this article, a review on conjugate gradient methods for unconstrained optimization is given. They are divided into early conjugate gradient methods, descent conjugate gradient methods, and sufficient descent conjugate gradient methods. Two general convergence theorems are provided for the conjugate gradient method assuming the descent property of each search direction. Some research issues on conjugate gradient methods are mentioned.

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Descent Property and Global Convergence of the Fletcher—Reeves Method with Inexact Line Search

Cited by 434 publications

References 4 publications

Exploiting damped techniques for nonlinear conjugate gradient methods

Exploiting damped techniques for nonlinear conjugate gradient methods

Symmetric Perry conjugate gradient method

Nonlinear Conjugate Gradient Methods

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