| Title:
|
Conjugate gradient algorithms for conic functions (English) |
| Author:
|
Lukšan, Ladislav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
31 |
| Issue:
|
6 |
| Year:
|
1986 |
| Pages:
|
427-440 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper contains a description and an analysis of two modifications of the conjugate gradient method for unconstrained minimization which find a minimum of the conic function after a finite number of steps. Moreover, further extension of the conjugate gradient method is given which is based on a more general class of the model functions. (English) |
| Keyword:
|
conjugate gradient method |
| Keyword:
|
unconstrained optimization |
| Keyword:
|
conic function |
| Keyword:
|
interpolations |
| Keyword:
|
algorithm |
| MSC:
|
65K05 |
| MSC:
|
65K10 |
| MSC:
|
90C20 |
| MSC:
|
90C30 |
| idZBL:
|
Zbl 0622.65045 |
| idMR:
|
MR0870480 |
| DOI:
|
10.21136/AM.1986.104222 |
| . |
| Date available:
|
2008-05-20T18:31:02Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104222 |
| . |
| Reference:
|
[1] J. Abaffy F. Sloboda: Imperfect conjugate gradient algorithms for extended quadratic functions.Numer. Math. 42, 97-105 (1983). MR 0716476, 10.1007/BF01400920 |
| Reference:
|
[2] E. M. L. Beale: A derivation of conjugate gradients.In: Nonlinear Optimization (Lootsma, F.A., ed.) New York: Academic Press 1972. Zbl 0279.65052, MR 0381696 |
| Reference:
|
[3] P. Bjørstad J. Nocedal: Analysis of a new algorithm for one-dimensional minimization.Computing 22, 93-100 (1979). MR 0620386, 10.1007/BF02246561 |
| Reference:
|
[4] W. R. Boland E. R. Kamgnia J. S. Kowalik: A conjugate-gradient optimization method invariant to nonlinear scaling.J. Optimization Theory Appl. 27, 221 - 230 (1979). MR 0529861, 10.1007/BF00933228 |
| Reference:
|
[5] W. C. Davidon: Conic approximations and collinear scalings for optimizers.SIAM J. Numer. Anal. 17, 268-281 (1980). Zbl 0424.65026, MR 0567273, 10.1137/0717023 |
| Reference:
|
[6] L. C. W. Dixon: Conjugate gradient algorithms: Quadratic termination properties without line searches.J. Inst. Math. Appl. 15, 9-18 (1975). MR 0368429, 10.1093/imamat/15.1.9 |
| Reference:
|
[7] R. Fletcher C. M. Reeves: Function minimization by conjugate gradients.Comput. J. 7, 149-154 (1964). MR 0187375, 10.1093/comjnl/7.2.149 |
| Reference:
|
[8] I. Fried: N-step conjugate gradient minimization scheme for nonquadratic functions.AIAA J. 9, 2286-2287 (1971). Zbl 0235.65040, MR 0359800, 10.2514/3.6507 |
| Reference:
|
[9] M. R. Hestenes E. Stiefel: The method of conjugate gradients for solving linear systems.J. Res. Nat. Bur. Standards, Section B 49, 409-436 (1952). MR 0060307, 10.6028/jres.049.044 |
| Reference:
|
[10] J. S. Kowalik E. R. Kamgnia W. R. Boland: An exponential function as a model for a conjugate gradient optimization method.J. Math. Anal. Appl. 67, 476-482 (1979). MR 0528701, 10.1016/0022-247X(79)90037-4 |
| Reference:
|
[11] M. J. D. Powell: Restart procedures for the conjugate gradient method.Math. Programming 12, 241-254 (1977). Zbl 0396.90072, MR 0478622, 10.1007/BF01593790 |
| Reference:
|
[12] J. E. Shirey: Minimization of extended quadratic functions.Numer. Math. 39, 157-161 (1982). Zbl 0491.65038, MR 0669312, 10.1007/BF01408690 |
| Reference:
|
[13] F. Sloboda: An imperfect conjugate gradient algorithm.Aplikace matematiky 27, 426-434 (1982). Zbl 0503.65017, MR 0678112 |
| Reference:
|
[14] F. Sloboda: A generalized conjugate gradient algorithm for minimization.Numer. Math. 35, 223-230 (1980). Zbl 0424.65033, MR 0585248, 10.1007/BF01396318 |
| Reference:
|
[15] D. C. Sorensen: The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization.SIAM J. Numer. Anal. 17, 84-114 (1980). Zbl 0428.65040, MR 0559465, 10.1137/0717011 |
| . |
