| Title:
|
Parallel method of conjugate directions for minimization (English) |
| Author:
|
Sloboda, Fridrich |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
20 |
| Issue:
|
6 |
| Year:
|
1975 |
| Pages:
|
436-446 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| . |
| Category:
|
math |
| . |
| Summary:
|
A nongradient method of conjugate directions for minimization id described. The method has the quadratic convergence property and is closely related to the method for linear systems, which makes it possible to use reduced algorithms when the corresponding matrix is sparse. () |
| MSC:
|
65K05 |
| MSC:
|
90C20 |
| idZBL:
|
Zbl 0326.90050 |
| idMR:
|
MR0395830 |
| DOI:
|
10.21136/AM.1975.103611 |
| . |
| Date available:
|
2008-05-20T18:02:46Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103611 |
| . |
| Reference:
|
[1] N. Adachi: On variable-metric algorithms.JOTA, б (1971), 391-410. Zbl 0203.48703, MR 0293814, 10.1007/BF00931977 |
| Reference:
|
[2] H. Y. Huang: Unified approach to quadratically convergent algorithms for minimization.JOTA, б (1970), 405-423. MR 0288939 |
| Reference:
|
[3] R. Fletcher M. J. D. Powell: A rapidly convergent descent method for minimization.Соmр. J., 2 (1963), 163-168. MR 0152116 |
| Reference:
|
[4] 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, 10.6028/jres.049.044 |
| Reference:
|
[5] R. Fletcher C. M. Reeves: Function minimization by conjugate gradients.Соmр. J. 2., (1964), 149-154. MR 0187375 |
| Reference:
|
[6] M. J. D. Powell: An efficient method for finding minimum of a function of several variables without calculating derivatives.Соmр. J., 7 (1964), 155-162. MR 0187376 |
| Reference:
|
[7] W. I. Zangwill: Minimizing a function without calculating derivatives.Com. J., 7 (1967), 293-296. Zbl 0189.48004, MR 0234614 |
| Reference:
|
[8] D. Chazan W. L. Miranker: A nongradient and parallel algorithm for unconstrained minimization.SIAM J. Control. 2 (1970), 207-217. MR 0275637 |
| Reference:
|
[9] W. W. Bradbury R. Fletcher: New iterative methods for solution of the eigenproblern.Numer. Math., 9 (1966), 259-267. MR 0219230, 10.1007/BF02162089 |
| Reference:
|
[10] R. Bellman R. Kalaba J. Lockett: Dynamic programming and ill-conditioned linear systems.J. of Math. Analysis and Applicat., 10 (1065), 206-215. MR 0171377 |
| Reference:
|
[11] E. J. Beltrami: An algorithmic approach to nonlinear analysis and optimization.Academic Press, New York, 1970. Zbl 0207.17202, MR 0270538 |
| Reference:
|
[12] H. Tokumaru N. Adachi K. Goto: Davidson's method for minimization problems in Hilbert space with an application to control problems.SIAM J. Control, 2 (1970), 163 - 178. MR 0272164 |
| Reference:
|
[13] J. Céa: Optimization théorie et algorithmes.Dunad, Paris, 1971. |
| Reference:
|
[14] D. M. Himmelblau: Decomposition of large-scale problems.North-Holl. publ. соmр., New York, 1973. Zbl 0254.90002, MR 0456435 |
| Reference:
|
[15] F. Sloboda: Parallel projection method for linear algebraic systems.to appear. Zbl 0398.65013, MR 0428695 |
| . |
