| Title:
|
Conjugate direction algorithms for extended conic functions (English) |
| Author:
|
Lukšan, Ladislav |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
22 |
| Issue:
|
1 |
| Year:
|
1986 |
| Pages:
|
31-46 |
| . |
| Category:
|
math |
| . |
| MSC:
|
49A55 |
| MSC:
|
49D07 |
| MSC:
|
65K05 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0597.65059 |
| idMR:
|
MR839343 |
| . |
| Date available:
|
2009-09-24T17:51:04Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125545 |
| . |
| Reference:
|
[1] J. Abaffy, F. Sloboda: Imperfect conjugate gradient algorithms for extended quadratic functions.Numer. Math. 42 (1983), 97-105. Zbl 0524.65045, MR 0716476 |
| Reference:
|
[2] P. Bjorstad, J. Nocedal: Analysis of a new algorithm for one-dimensional minimization.Computing 22 (1979), 93-100. Zbl 0401.65041, MR 0620386 |
| Reference:
|
[3] C. G. Broyden: Quasi-Newton methods and their application to function minimization.Math. Comp. 21 (1967), 368-381. MR 0224273 |
| Reference:
|
[4] W. C. Davidon: Variable Metric Method for Minimization.Report ANL-5990 Rev., Argonne National Laboratories, Argonne, IL, 1959. |
| Reference:
|
[5] W. C. Davidon: Conic approximations and collinear scalings for optimizers.SIAM J. Numer. Anal. 17 (1980), 268-281. Zbl 0424.65026, MR 0567273 |
| Reference:
|
[6] E. J. Davison, P. Wong: A robust algorithm that minimizes 1-functions.Automatica 11 (1975), 287-308. MR 0406520 |
| Reference:
|
[7] L. C. W. Dixon: Conjugate directions without linear searches.Inst. Math. Appl. 11 (1973), 317-328. Zbl 0259.65060, MR 0336995 |
| Reference:
|
[8] L. C. W. Dixon: Conjugate gradient algorithm: quadratic termination properties without line searches.Inst. Math. Appl. 15 (1975), 9-18. MR 0368429 |
| Reference:
|
[9] J. Flachs: On the convergence, invariance, and related aspects of a modification of Huang's algorithm.Optim. Theory Appl. 37 (1982), 315-341. Zbl 0462.65042, MR 0663527 |
| Reference:
|
[10] R. Fletcher, M. J. D. Powell. : A rapidly convergent descent method for minimization.Comput. J. 6 (1963), 163-168. Zbl 0132.11603, MR 0152116 |
| Reference:
|
[11] R. Fletcher, C. M. Reeves: Function minimization by conjugate gradients.Comput. J. 7 (1964), 149-154. Zbl 0132.11701, MR 0187375 |
| Reference:
|
[12] D. Goldfarb: Extension of Davidon's variable metric method to maximization under linear inequality and equality constraints.SIAM J. Appl. Math. 17 (1969), 739-763. Zbl 0185.42602, MR 0290799 |
| Reference:
|
[13] M. R. Hestenes, E. Stiefel: The method of conjugate gradients for solving linear systems.J. Res. Nat. Bur. Standards 49 (1952), 409-436. MR 0060307 |
| Reference:
|
[14] H. Y. Huang: Method of Dual Matrices for Function Minimization.Aero-Astronautic Report No. 88, Rice University, Houston, TX, 1972. Zbl 0254.65044 |
| Reference:
|
[15] M. L. Lenard: Accelerated Conjugate Direction Methods for Unconstrained Optimization.Technical Report No. MRC-1591, University of Wisconsin, Madison, WI, 1976. |
| Reference:
|
[16] L. Lukšan: Conjugate gradient algorithms for conic functions.Aplikace matemat. (to appear). MR 0870480 |
| Reference:
|
[17] L. Lukšan: Variable metric methods for a class of extended conic functions.Kybernetika 21 (1985), 96-107. MR 0797323 |
| Reference:
|
[18] L. Nazareth: A conjugate direction algorithm without line searches.J. Optim. Theory Appl. 23 (1977), 373-387. Zbl 0348.65061, MR 0525743 |
| Reference:
|
[19] J. E. Shirey: Minimization of extended quadratic functions.Numer. Math. 39 (1982), 157-161. Zbl 0491.65038, MR 0669312 |
| Reference:
|
[20] F. Sloboda: An imperfect conjugate gradient algorithm.Aplikace matematiky 27 (1982), 426-434. Zbl 0503.65017, MR 0678112 |
| Reference:
|
[21] F. Sloboda: A generalized conjugate gradient algorithm for minimization.Numer. Math. 35 (1980), 223-230. Zbl 0424.65033, MR 0585248 |
| Reference:
|
[22] D. C. Sorensen: The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization.SIAM J. Numer. Anal. 17 (1980), 84-114. Zbl 0428.65040, MR 0559465 |
| Reference:
|
[23] E. Spedicato: A variable-metric method for function minimization derived from invariancy to nonlinear scaling.J. Optim. Theory Appl. 20 (1976), 315-329. Zbl 0316.90066, MR 0426854 |
| Reference:
|
[24] G. Zoutendijk: Methods of Feasible Directions.Elsevier, Amsterdam 1960. Zbl 0097.35408 |
| . |
