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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  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
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  9. M. R. Hestenes E. Stiefel, 10.6028/jres.049.044, J. Res. Nat. Bur. Standards, Section B 49, 409-436 (1952). (1952) Zbl0048.09901MR0060307DOI10.6028/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) Zbl0416.65045MR0528701DOI10.1016/0022-247X(79)90037-4
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  13. F. Sloboda, An imperfect conjugate gradient algorithm, Aplikace matematiky 27, 426-434 (1982). (1982) Zbl0503.65017MR0678112
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