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Zbl 0638.65055
Barzilai, Jonathan; Borwein, Jonathan M.
Two-point step size gradient methods. (English)
[J] IMA J. Numer. Anal. 8, No.1, 141-148 (1988). ISSN 0272-4979; ISSN 1464-3642/e

For the steepest-descent method two-point step sizes are derived by approximating the secant equation. A convergence analysis of these methods made in the two-dimensional quadratic case. According the numerical examples, these algorithms achieve better performance and cheaper computation than the classical steepest-descent method.
[J.Abaffy]

MSC 2000:: *65K05 Mathematical programming (numerical methods)
65K10 Optimization techniques (numerical methods)
90C30 Nonlinear programming

Keywords: unconstrained minimization secant method; steepest-descent method; convergence; numerical examples

Cited in: Zbl 1259.65076 Zbl 1235.65027 Zbl 1217.65107 Zbl 1191.65020 Zbl 1179.65067 Zbl 1170.65318 Zbl 1166.65400 Zbl 1165.65033 Zbl 1172.90509 Zbl 1152.65071 Zbl 1101.65067 Zbl 1087.65539 Zbl 1071.65084 Zbl 1068.65073 Zbl 1056.65055 Zbl 1002.65069 Zbl 0940.65032 Zbl 0898.90119 Zbl 0861.65025 Zbl 0778.65045

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