Local and superlinear convergence of quasi-Newton methods based on modified secant conditions

Yabe, Hiroshi; Ogasawara, Hideho; Yoshino, Masayuki

doi:10.1016/j.cam.2006.05.018

Cited by 39 publications

(14 citation statements)

References 11 publications

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“…is sufficiently far away from one, this ratio seems to measure of quality of yk compared to B s k k reasonably well (see for example [17]). We now consider a modified technique for y k .…”

Section: = -+mentioning

confidence: 94%

A modified BFGS method for solving symmetric nonlinear equations

Bidabadi¹

2014

Journal of Interdisciplinary Mathematics

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“…is sufficiently far away from one, this ratio seems to measure of quality of yk compared to B s k k reasonably well (see for example [17]). We now consider a modified technique for y k .…”

Section: = -+mentioning

confidence: 94%

A modified BFGS method for solving symmetric nonlinear equations

Bidabadi¹

2014

Journal of Interdisciplinary Mathematics

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“…In order to unify (2) and (6) format, Hiroshi and Yabe, etc [6]., introduced a parameter to form the following quasi Newton equation. 1 T…”

Section: Wang Bao and Wang Yanxinmentioning

confidence: 99%

“…When k  =0 or 1, it is corresponding to the quasi Newton equation (2) or quasi Newton equation (6).…”

Section: Wang Bao and Wang Yanxinmentioning

confidence: 99%

Sub-Direction Parallel Search Quasi-Newton Algorithm

Bao¹,

Yanxin²

2018

IJMO

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Advantages and disadvantages in a sequence of unconstrained optimization method are basically compared. The original constrained problem is replaced by a sequence of unconstrained sub-problems through the augmented Lagrangian multiplier method. The unconstrained sub-problems are solved by BFGS method and the sub-direction parallel search quasi-Newton algorithm. Efficiency of this method is compared. The results of numerical tests show that the calculation time of the sub-direction parallel search quasi-Newton algorithm is short and it can solve engineering optimization problems completely.

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“…Zhang et al [30] and Zhang and Xu [29] used a quadratic interpolation for g and proposed another modified secant equation with a higher order accuracy in approximating the curvature of the objective function. In order to adoptively switch the standard secant equation to the modified secant equation proposed in [29,30], slight revisions have been made by Yabe et al [25,26] and Babaie-Kafaki et al [2] by embedding a parameter on this equation. All the mentioned methods in [23,27,29,30] use both the gradient and function values available at the current iteration.…”

Section: Introductionmentioning

confidence: 97%

A modified BFGS algorithm based on a hybrid secant equation

Babaie-Kafaki

2011

Sci. China Math.

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By making a convex combination of the modified secant equations proposed by Yuan and Wei et al., a hybrid secant equation and also, a modified BFGS algorithm is proposed. The hybridization parameter is effectively computed using the available information of recent iterations. Under proper conditions, it is shown that the proposed algorithm is globally, locally and superlinearly convergent. By using the performance profile introduced by Dolan and Moré, a comparison between the implementations of the proposed algorithm and two efficient modified BFGS algorithms proposed by Yuan and Wei et al., on a set of unconstrained optimization test problems from the CUTEr collection, is done. Numerical results demonstrating the efficiency of the proposed modified BFGS algorithm are reported. Keywords unconstrained optimization, hybrid secant equation, BFGS update, global convergence, local and superlinear convergence MSC(2000): 90C53, 49M37, 65K05 Citation: Babaie-Kafaki S. A modified BFGS algorithm based on a hybrid secant equation.

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Local and superlinear convergence of quasi-Newton methods based on modified secant conditions

Cited by 39 publications

References 11 publications

A modified BFGS method for solving symmetric nonlinear equations

A modified BFGS method for solving symmetric nonlinear equations

Sub-Direction Parallel Search Quasi-Newton Algorithm

A modified BFGS algorithm based on a hybrid secant equation

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