| Title:
|
Variable metric method with limited storage for large-scale unconstrained minimization (English) |
| Author:
|
Lukšan, Ladislav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
18 |
| Issue:
|
6 |
| Year:
|
1982 |
| Pages:
|
517-528 |
| . |
| Category:
|
math |
| . |
| MSC:
|
65K05 |
| MSC:
|
65K10 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0514.65049 |
| idMR:
|
MR707399 |
| . |
| Date available:
|
2009-09-24T17:30:59Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124855 |
| . |
| Reference:
|
[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. Zbl 0279.65052, MR 0381696 |
| Reference:
|
[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 0226.90045 |
| Reference:
|
[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 0433870 |
| Reference:
|
[4] A. G. Buckley: A combined conjugate gradient quasi-Newton minization algorithm.Math. Programming 15 (1978), 2, 200-210. MR 0509962 |
| Reference:
|
[5] A. G. Buckley: Extending the relationship between the conjugate gradient and BFGS algorithms.Math. Programming 75 (1978), 3, 343-348. Zbl 0393.90075, MR 0514615 |
| Reference:
|
[6] R. Fletcher C. M. Reeves: Function minimization by conjugate gradients.Comput. J. 7 (1964), 2, 149-154. MR 0187375 |
| Reference:
|
[7] R. Fletcher: A new approach to variable metric algorithms.Comput. J. 13 (1970), 3, 317- 322. |
| Reference:
|
[8] D. Goldfarb: A family of variable metric algorithms derived by variational means.Math. Comp. 24 (1970), 109, 23-26. MR 0258249 |
| Reference:
|
[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 0060307 |
| Reference:
|
[10] L. Lukšan: Software package for optimization and nonlinear approximation.Proc. of 2nd IFAC/IFIP Symposium on software for computer control, Prague 1979. |
| Reference:
|
[11] L. Nazareth: A relationship between the BFGS and conjugate gradient algorithms.SIAM J. Numer. Anal. 16 (1979), 5, 794-800. MR 0543969 |
| Reference:
|
[12] L. Nazareth: A conjugate direction algorithm without line searches.J. Optim. Theory Appl. 23 (1977), 3, 373-387. Zbl 0348.65061, MR 0525743 |
| Reference:
|
[13] J. Nocedal: Updating quasi-Newton matrices with limited storage.Math. Comp. 35 (1980), 151, 773-782. Zbl 0464.65037, MR 0572855 |
| Reference:
|
[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 0388773 |
| Reference:
|
[15] A. Perry: A modified conjugate gradient algorithm.Oper. Res. 26 (1978), 6, 1073 - 1078. Zbl 0419.90074, MR 0514875 |
| Reference:
|
[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 0255025 |
| Reference:
|
[17] M. J. D. Powell: Restart procedure for the conjugate gradient method.Math. Programming 72 (1977), 2, 241-254. MR 0478622 |
| Reference:
|
[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 0165655 |
| Reference:
|
[19] D. F. Shanno: Conditioning of quasi-Newton methods for function minimization.Math. Comp. 24 (1970), 111, 647-656. MR 0274029 |
| Reference:
|
[20] D. F. Shanno: Conjugate gradient methods with inexact searches.Math. Oper. Res. 3 (1978), 3, 244-256. Zbl 0399.90077, MR 0506662 |
| Reference:
|
[21] D. F. Shanno K. H. Phua: Matrix conditioning and nonlinear optimization.Math. Programming 14 (1978), 2, 149-160. MR 0474819 |
| . |
