# A conjugate gradient method with quasi-Newton approximation

Applicationes Mathematicae (2000)

- Volume: 27, Issue: 2, page 153-165
- ISSN: 1233-7234

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topKoko, Jonas. "A conjugate gradient method with quasi-Newton approximation." Applicationes Mathematicae 27.2 (2000): 153-165. <http://eudml.org/doc/219264>.

@article{Koko2000,

abstract = {The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.},

author = {Koko, Jonas},

journal = {Applicationes Mathematicae},

keywords = {Newton and quasi-Newton methods; unconstrained high-dimensional optimization; conjugate gradient methods; numerical examples; conjugate gradient method; minimization algorithm; quasi-Newton approximation; convergence},

language = {eng},

number = {2},

pages = {153-165},

title = {A conjugate gradient method with quasi-Newton approximation},

url = {http://eudml.org/doc/219264},

volume = {27},

year = {2000},

}

TY - JOUR

AU - Koko, Jonas

TI - A conjugate gradient method with quasi-Newton approximation

JO - Applicationes Mathematicae

PY - 2000

VL - 27

IS - 2

SP - 153

EP - 165

AB - The conjugate gradient method of Liu and Storey is an efficient minimization algorithm which uses second derivatives information, without saving matrices, by finite difference approximation. It is shown that the finite difference scheme can be removed by using a quasi-Newton approximation for computing a search direction, without loss of convergence. A conjugate gradient method based on BFGS approximation is proposed and compared with existing methods of the same class.

LA - eng

KW - Newton and quasi-Newton methods; unconstrained high-dimensional optimization; conjugate gradient methods; numerical examples; conjugate gradient method; minimization algorithm; quasi-Newton approximation; convergence

UR - http://eudml.org/doc/219264

ER -

## References

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- [7] Y. F. Hu and C. Storey, Efficient generalized conjugate gradient algorithms, Part 2: Implementation, J. Optim. Theory Appl. 69 (1991), 139-152.
- [8] Y. F. Hu and C. Storey, Preconditioned low-order Newton methods, ibid. 79 (1993), 311-331.
- [9] Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, Part 1: Theory, ibid. 69 (1991), 129-137.
- [10] J. L. Nazareth, The method of successive affine reduction for nonlinear minimization, Math. Programming 35 (1985), 97-109. Zbl0621.90076
- [11] J. L. Nazareth, Conjugate gradient methods less dependent on conjugacy, SIAM Rev. 28 (1986), 501-511. Zbl0625.90077
- [12] E. Polak and G. Ribière, Note sur la convergence des méthodes de directions conjuguées, RAIRO Rech. Opér. 16 (1969), 35-43. Zbl0174.48001

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