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Acceleration de la convergence de la methode de la plus forte pente

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Języki publikacji
FR
Abstrakty
EN
Let (P) be the following problem of optimization without constraints (P) min{f(x) : x is an element of Rn}. We study in this paper an algorithm which acceleretes the convergence of the steepest descent method.
Wydawca
Rocznik
Strony
169--181
Opis fizyczny
BIbliogr. 15 poz.
Twórcy
autor
autor
  • Departement de Mathematiques Universite Badji Mokhtar Annaba B.P. 12, 23000 Annaba, Algerie, rabenzine@yahoo.fr
Bibliografia
  • [1] A. C. Aitken, On Bernoulli's numerical solution of algebraic equations, Proc. Roy. Soc. Edinburgh, 46 (1926), 289-305.
  • [2] M. S. Bazaraa, H. D. Sherali, C. M. Shetty, Nonlinear Programing, John Wiley & Sons, New York, (1993).
  • [3] C. Brezinski, Acceleration de la convergence en analyse numérique, Lecture Notes in Mathematics, 584, Springer Verlag (1977).
  • [4] C. G. Broyden, J. E. Dennis, Jr., J. J. Moré, On the local and superlinear convergence of quasi-Newton methods, J. Inst. Math. Appl. 12 (1973), 223-246.
  • [5] J. E. Dennis, Jr., J. J. Moré A characterization of superlinear convergence and its application to quasi-Newton methods, Math. Comp. 28 (1974), 549-560.
  • [6] J. E. Dennis, J. J. Moré, Quasi-Newton methods, motivation and theory, SIAM Rev. 19 (1977), 46-89.
  • [7] L. C. W. Dixon, Variable metric algorithms : necessary and sufficient conditions for identical behavior on nonquadratic functions, J. Opt. Theory Appl. 10 (1972), 34-40
  • [8] R. Fletcher, Practical Methods of Optimization, Second Edition, John Wiley & Sons, Chichester, 1987.
  • [9] R. Fletcher, An Overview of Unconstrained Optimization, in Algorithms for Continuous Optimization: the State of Art, E .Spedicato, ed., Kluwer Academic Publishers, 1994.
  • [10] G. E. Forsythe, On the asymptotic directions of the s-dimentional optimum gradient method, Num. Math. 11, pp. 57-76.
  • [11] P. E. Gill, W. Marray, Quasi-Newton Methods for unconstrained optimization, J. Inst. Math. Appl. 9 (1972), 91-108.
  • [12] A. Griewank, The global convergence of partitioned BFGS on problems with convex decompositions and Lipschitz gradients, Math. Prog. 50 (1991), 141-175.
  • [13] M. J. D. Powell, On the convergence of the variable metric algorithms, J. Inst. Math. Appl. 7 (1971), 21-36.
  • [14] M. J. D. Powel, Some global convergence properties of variable metric algorithms for minimization without exact line searches, in Nonlinear Programming, SIAM -AMS Proceedings, Vol. IX, R. W. Cottle, and C. E. Lemke (eds.), SIAM 1976.
  • [15] P. Wynn, On a device for computing the em(Sn) transformation, M.T.A.C., 10, (1956), 91-96.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0021-0018
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