Conjugate gradient algorithms for conic functions

Ladislav Lukšan

Aplikace matematiky (1986)

  • Volume: 31, Issue: 6, page 427-440
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Lukšan, Ladislav. "Conjugate gradient algorithms for conic functions." Aplikace matematiky 31.6 (1986): 427-440. <http://eudml.org/doc/15468>.

@article{Lukšan1986,
abstract = {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.},
author = {Lukšan, Ladislav},
journal = {Aplikace matematiky},
keywords = {conjugate gradient method; unconstrained optimization; conic function; interpolations; algorithm; conjugate gradient method; unconstrained optimization; conic function; interpolations; algorithm},
language = {eng},
number = {6},
pages = {427-440},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Conjugate gradient algorithms for conic functions},
url = {http://eudml.org/doc/15468},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Lukšan, Ladislav
TI - Conjugate gradient algorithms for conic functions
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 6
SP - 427
EP - 440
AB - 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.
LA - eng
KW - conjugate gradient method; unconstrained optimization; conic function; interpolations; algorithm; conjugate gradient method; unconstrained optimization; conic function; interpolations; algorithm
UR - http://eudml.org/doc/15468
ER -

References

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  1. J. Abaffy F. Sloboda, 10.1007/BF01400920, Numer. Math. 42, 97-105 (1983). (1983) MR0716476DOI10.1007/BF01400920
  2. E. M. L. Beale, A derivation of conjugate gradients, In: Nonlinear Optimization (Lootsma, F.A., ed.) New York: Academic Press 1972. (1972) Zbl0279.65052MR0381696
  3. P. Bjørstad J. Nocedal, 10.1007/BF02246561, Computing 22, 93-100 (1979). (1979) MR0620386DOI10.1007/BF02246561
  4. W. R. Boland E. R. Kamgnia J. S. Kowalik, 10.1007/BF00933228, J. Optimization Theory Appl. 27, 221 - 230 (1979). (1979) MR0529861DOI10.1007/BF00933228
  5. W. C. Davidon, 10.1137/0717023, SIAM J. Numer. Anal. 17, 268-281 (1980). (1980) Zbl0424.65026MR0567273DOI10.1137/0717023
  6. L. C. W. Dixon, 10.1093/imamat/15.1.9, J. Inst. Math. Appl. 15, 9-18 (1975). (1975) MR0368429DOI10.1093/imamat/15.1.9
  7. R. Fletcher C. M. Reeves, 10.1093/comjnl/7.2.149, Comput. J. 7, 149-154 (1964). (1964) MR0187375DOI10.1093/comjnl/7.2.149
  8. I. Fried, 10.2514/3.6507, AIAA J. 9, 2286-2287 (1971). (1971) Zbl0235.65040MR0359800DOI10.2514/3.6507
  9. M. R. Hestenes E. Stiefel, 10.6028/jres.049.044, J. Res. Nat. Bur. Standards, Section B 49, 409-436 (1952). (1952) MR0060307DOI10.6028/jres.049.044
  10. J. S. Kowalik E. R. Kamgnia W. R. Boland, 10.1016/0022-247X(79)90037-4, J. Math. Anal. Appl. 67, 476-482 (1979). (1979) MR0528701DOI10.1016/0022-247X(79)90037-4
  11. M. J. D. Powell, 10.1007/BF01593790, Math. Programming 12, 241-254 (1977). (1977) Zbl0396.90072MR0478622DOI10.1007/BF01593790
  12. J. E. Shirey, 10.1007/BF01408690, Numer. Math. 39, 157-161 (1982). (1982) Zbl0491.65038MR0669312DOI10.1007/BF01408690
  13. F. Sloboda, An imperfect conjugate gradient algorithm, Aplikace matematiky 27, 426-434 (1982). (1982) Zbl0503.65017MR0678112
  14. F. Sloboda, 10.1007/BF01396318, Numer. Math. 35, 223-230 (1980). (1980) Zbl0424.65033MR0585248DOI10.1007/BF01396318
  15. D. C. Sorensen, 10.1137/0717011, SIAM J. Numer. Anal. 17, 84-114 (1980). (1980) Zbl0428.65040MR0559465DOI10.1137/0717011

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