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A class of exponential quadratically convergent iterative formulae for unconstrained optimization. (English) Zbl 1121.65067

A nonlinear unconstraint optimization problem with an objective function depending: on one variable is considered. Three modifications of the Newton method for solving this problem are proposed. Each of the methods has an exponential iteration formula. It is proved that the proposed methods converge to the optimum solution with a quadratic order of convergence in a neighborhood of the optimum. The efficiency of the methods is analyzed using a criterion based on a comparison to the classical Newton method. Numerical experiments reported in the concluding part of the paper support obtained theoretical results and indicate that one of the exponential iterative formulae is from the point of view of its efficiency comparable to the classical Newton method.

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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References:

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