Geodesic
Conjugate gradient algorithms for conic functions
Applications of Mathematics, Tome 31 (1986) no. 6, pp. 427-440
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1986.104222
Classification : 65K05, 65K10, 90C20, 90C30
Keywords: conjugate gradient method; unconstrained optimization; conic function; interpolations; algorithm 
@article{10_21136_AM_1986_104222,
     author = {Luk\v{s}an, Ladislav},
     title = {Conjugate gradient algorithms for conic functions},
     journal = {Applications of Mathematics},
     pages = {427--440},
     year = {1986},
     volume = {31},
     number = {6},
     doi = {10.21136/AM.1986.104222},
     mrnumber = {0870480},
     zbl = {0622.65045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1986.104222/}
}
TY  - JOUR
AU  - Lukšan, Ladislav
TI  - Conjugate gradient algorithms for conic functions
JO  - Applications of Mathematics
PY  - 1986
SP  - 427
EP  - 440
VL  - 31
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1986.104222/
DO  - 10.21136/AM.1986.104222
LA  - en
ID  - 10_21136_AM_1986_104222
ER  - 
%0 Journal Article
%A Lukšan, Ladislav
%T Conjugate gradient algorithms for conic functions
%J Applications of Mathematics
%D 1986
%P 427-440
%V 31
%N 6
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1986.104222/
%R 10.21136/AM.1986.104222
%G en
%F 10_21136_AM_1986_104222
Lukšan, Ladislav. Conjugate gradient algorithms for conic functions. Applications of Mathematics, Tome 31 (1986) no. 6, pp. 427-440. doi: 10.21136/AM.1986.104222

[1] J. Abaffy F. Sloboda: Imperfect conjugate gradient algorithms for extended quadratic functions. Numer. Math. 42, 97-105 (1983). | DOI | MR

[2] E. M. L. Beale: A derivation of conjugate gradients. In: Nonlinear Optimization (Lootsma, F.A., ed.) New York: Academic Press 1972. | MR | Zbl

[3] P. Bjørstad J. Nocedal: Analysis of a new algorithm for one-dimensional minimization. Computing 22, 93-100 (1979). | DOI | MR

[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). | DOI | MR

[5] W. C. Davidon: Conic approximations and collinear scalings for optimizers. SIAM J. Numer. Anal. 17, 268-281 (1980). | DOI | MR | Zbl

[6] L. C. W. Dixon: Conjugate gradient algorithms: Quadratic termination properties without line searches. J. Inst. Math. Appl. 15, 9-18 (1975). | DOI | MR

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

[8] I. Fried: N-step conjugate gradient minimization scheme for nonquadratic functions. AIAA J. 9, 2286-2287 (1971). | DOI | MR | Zbl

[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). | DOI | MR

[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). | DOI | MR

[11] M. J. D. Powell: Restart procedures for the conjugate gradient method. Math. Programming 12, 241-254 (1977). | DOI | MR | Zbl

[12] J. E. Shirey: Minimization of extended quadratic functions. Numer. Math. 39, 157-161 (1982). | DOI | MR | Zbl

[13] F. Sloboda: An imperfect conjugate gradient algorithm. Aplikace matematiky 27, 426-434 (1982). | MR | Zbl

[14] F. Sloboda: A generalized conjugate gradient algorithm for minimization. Numer. Math. 35, 223-230 (1980). | DOI | MR | Zbl

[15] D. C. Sorensen: The Q-superlinear convergence of a collinear scaling algorithm for unconstrained optimization. SIAM J. Numer. Anal. 17, 84-114 (1980). | DOI | MR | Zbl

Cité par Sources :