Geodesic
Variable metric method with limited storage for large-scale unconstrained minimization
Kybernetika, Tome 18 (1982) no. 6, pp. 517-528 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 65K05, 65K10, 90C30 
@article{KYB_1982_18_6_a3,
     author = {Luk\v{s}an, Ladislav},
     title = {Variable metric method with limited storage for large-scale unconstrained minimization},
     journal = {Kybernetika},
     pages = {517--528},
     year = {1982},
     volume = {18},
     number = {6},
     mrnumber = {707399},
     zbl = {0514.65049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_1982_18_6_a3/}
}
TY  - JOUR
AU  - Lukšan, Ladislav
TI  - Variable metric method with limited storage for large-scale unconstrained minimization
JO  - Kybernetika
PY  - 1982
SP  - 517
EP  - 528
VL  - 18
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_1982_18_6_a3/
LA  - en
ID  - KYB_1982_18_6_a3
ER  - 
%0 Journal Article
%A Lukšan, Ladislav
%T Variable metric method with limited storage for large-scale unconstrained minimization
%J Kybernetika
%D 1982
%P 517-528
%V 18
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_1982_18_6_a3/
%G en
%F KYB_1982_18_6_a3
Lukšan, Ladislav. Variable metric method with limited storage for large-scale unconstrained minimization. Kybernetika, Tome 18 (1982) no. 6, pp. 517-528. http://geodesic.mathdoc.fr/item/KYB_1982_18_6_a3/

[1 ] E. M. L. Beale: A derivation of conjugate gradients. In: Numerical Methods for Non-linear Optimization (F. A. Lootsma ed.), Academic Press, London 1972, 39-43. | MR | Zbl

[2] M. C. Biggs: Minimization algorithms making use of non-quadratic properties of the objective function. J. Inst. Math. Appl. 5 (1971), 3, 315 - 327. | Zbl

[3] C. G.Broyden: The convergence of a class of double rank minimization algorithms 2. The new algorithm. J. Inst. Math. Appl. 6 (1970), 3, 222-231. | MR

[4] A. G. Buckley: A combined conjugate gradient quasi-Newton minization algorithm. Math. Programming 15 (1978), 2, 200-210. | MR

[5] A. G. Buckley: Extending the relationship between the conjugate gradient and BFGS algorithms. Math. Programming 75 (1978), 3, 343-348. | MR | Zbl

[6] R. Fletcher C. M. Reeves: Function minimization by conjugate gradients. Comput. J. 7 (1964), 2, 149-154. | MR

[7] R. Fletcher: A new approach to variable metric algorithms. Comput. J. 13 (1970), 3, 317- 322.

[8] D. Goldfarb: A family of variable metric algorithms derived by variational means. Math. Comp. 24 (1970), 109, 23-26. | MR

[9] M. R. Hestenes E. Stiefel: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Standards 49 (1952), 6, 409-439. | MR

[10] L. Lukšan: Software package for optimization and nonlinear approximation. Proc. of 2nd IFAC/IFIP Symposium on software for computer control, Prague 1979.

[11] L. Nazareth: A relationship between the BFGS and conjugate gradient algorithms. SIAM J. Numer. Anal. 16 (1979), 5, 794-800. | MR

[12] L. Nazareth: A conjugate direction algorithm without line searches. J. Optim. Theory Appl. 23 (1977), 3, 373-387. | MR | Zbl

[13] J. Nocedal: Updating quasi-Newton matrices with limited storage. Math. Comp. 35 (1980), 151, 773-782. | MR | Zbl

[14] S. S. Oren D. G. Luenberger: Self-scaling variable metric SSVM algorithms 1. Criteria and sufficient conditions for scaling a class of algorithms. Management Sci. 20 (1974), 5, 845-862. | MR

[15] A. Perry: A modified conjugate gradient algorithm. Oper. Res. 26 (1978), 6, 1073 - 1078. | MR | Zbl

[16] E. Polak G. Ribiere: Note sur la convergence de methodes des directions conjugees. Revue Fr. Inf. Rech. Oper. 16-R1 (1969), 35-43. | MR

[17] M. J. D. Powell: Restart procedure for the conjugate gradient method. Math. Programming 72 (1977), 2, 241-254. | MR

[18] B. V. Shah R. J. Buehleг O. Kempthorne: Some algorithms for minimizing a function of several variables. SIAM J. 12 (1964), 1, 74-92. | MR

[19] D. F. Shanno: Conditioning of quasi-Newton methods for function minimization. Math. Comp. 24 (1970), 111, 647-656. | MR

[20] D. F. Shanno: Conjugate gradient methods with inexact searches. Math. Oper. Res. 3 (1978), 3, 244-256. | MR | Zbl

[21] D. F. Shanno K. H. Phua: Matrix conditioning and nonlinear optimization. Math. Programming 14 (1978), 2, 149-160. | MR