A rapidly convergent five-point algorithm for univariate minimization

A rapidly convergent five-point algorithm for univariate minimization

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Article ID: iaor19951887
Country: Netherlands
Volume: 62
Issue: 2
Start Page Number: 299
End Page Number: 319
Publication Date: Nov 1993
Journal: Mathematical Programming
Authors: ,
Abstract:

This paper presents an algorithm for minimizing a function of one variable which uses function, but not derivative, values at five-points to generate each iterate. It employs quadratic and polyhedral approximations together with a safeguard. The basic method without the safeguard exhibits a type of better than linear convergence for certain piecewise twice continuously differentiable functions. The safeguard guarantees convergence to a stationary point for very general functions and preserves the better than linear convergence of the basic method.

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