Two-point step size gradient methods. (English) Zbl 0638.65055

Barzilai, Jonathan; Borwein, Jonathan M.

IMA J. Numer. Anal. 8, No. 1, 141-148 (1988).

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.

Reviewer: J.Abaffy

MSC:

65K05	Numerical mathematical programming methods
65K10	Numerical optimization and variational techniques
90C30	Nonlinear programming

Keywords:

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