Implicit extra-update multi-step quasi-Newton methods

Moghrabi, Issam A. R.

doi:10.1504/ijor.2017.081472

Cited by 6 publications

(10 citation statements)

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“…Such choices are sensitively influential to the structure of the interpolating curve. In this paper, the choice based on the so-called Accumulative Approach is elected due to its numerical merits [18,19].…”

Section: Multi-step Quasi-newton Methodsmentioning

confidence: 99%

“…Choices considered for the matrix M include M = B i , M = B i+1 and M = I, [12,18,19]. For the 2-step methods, the Hessian approximation is updated to generally satisfy:…”

Section: Multi-step Quasi-newton Methodsmentioning

confidence: 99%

“…The methods tested here implement the same line search strategy with the choices ρ 1 = 0.0001 and ρ 1 = 0.88 in (18)and (19), respectively. The termination criterion used for the two methods tested here is g(x i ) ≤ 10 −5 .…”

Section: Numerical Computationsmentioning

confidence: 99%

See 2 more Smart Citations

New Two-Step Conjugate Gradient Method for Unconstrained Optimization

Moghrabi¹

2020

Int. J. of Appl. Math.

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Section: Multi-step Quasi-newton Methodsmentioning

confidence: 99%

“…Choices considered for the matrix M include M = B i , M = B i+1 and M = I, [12,18,19]. For the 2-step methods, the Hessian approximation is updated to generally satisfy:…”

Section: Multi-step Quasi-newton Methodsmentioning

confidence: 99%

See 1 more Smart Citation

New Two-Step Conjugate Gradient Method for Unconstrained Optimization

Moghrabi¹

2020

Int. J. of Appl. Math.

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“…Such choices are sensitively influential to the structure of the interpolating curve. In this paper, the choice based on the so-called Accumulative Approach [12,17,18] is elected due to its numerical merits.…”

Section: Multi-step Quasi-newton Methodsmentioning

confidence: 99%

“…Choices considered for the matrix M (see [12,17,18] More generally, (8) may be modified by plugging in a scaling parameter, that offers more control in this context since setting the scalar to zero provides convenient switching to the standard secant one-step update. Therefore,…”

Section: Multi-step Quasi-newton Methodsmentioning

confidence: 99%

New Two-step Conjugate Gradient Method for Unconstrained Optimization

2020

International Journal of Mathematics and Computers in Simulation

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Two-step methods are secant-like techniques of the quasi-Newton type that, unlike the classical methods, construct nonlinear alternatives to the quantities used in the so-called Secant equation. Two-step methods instead incorporate data available from the two most recent iterations and thus create an alternative to the Secant equation with the intention of creating better Hessian approximations that induce faster convergence to the minimizer of the objective function. Such methods, based on reported numerical results published in several research papers related to the subject, have introduced substantial savings in both iteration and function evaluation counts. Encouraged by the successful performance of the methods, we explore in this paper employing them in developing a new Conjugate Gradient (CG) algorithm. CG methods gain popularity on big problems and in situations when memory resources are scarce. The numerical experimentations on the new methods are encouraging and open venue for further investigation of such techniques to explore their merits in a multitude of applications.

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On the local convergence study for an efficient k-step iterative method

Amat

Argyros

Busquier

et al. 2018

Journal of Computational and Applied Mathematics

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This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. The methods have high order of convergence but only using first order derivatives. Moreover only one LU decomposition is required in each iteration. In particular, the methods are real alternatives to the classical Newton method. We present a local convergence analysis based on hypotheses only on the first derivative. This type of local results were usually proved based on hypotheses on the derivative of order higher than two although only the first derivative appears in these type of methods [2,22,24]. We apply these methods to an equation related to the nonlinear complementarity problem. Finally, we find the most efficient method in the family for this problem and we perform a theoretical and a numerical study for it.

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Implicit extra-update multi-step quasi-Newton methods

Cited by 6 publications

References 0 publications

New Two-Step Conjugate Gradient Method for Unconstrained Optimization

New Two-Step Conjugate Gradient Method for Unconstrained Optimization

New Two-step Conjugate Gradient Method for Unconstrained Optimization

On the local convergence study for an efficient k-step iterative method

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