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Convergence properties of the Fletcher-Reeves method. (English) Zbl 0851.65049
This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. It is proven, that a kind of inexact line search condition can ensure the convergence of the FR method. Several examples are constructed to show that, if the search conditions are relaxed, the FR method may produce an ascent search direction, which implies that the result of the authors cannot be improved.
Reviewer: J.Terno (Dresden)

MSC:
65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
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