quadraticinterpolation: Quadratic Interpolation Method.

In brunasqz/NonlinearOpMethods: Nonlinear Optimization Methods

Description

quadraticinterpolation is a one-dimensional minimization method that finds the minimizing step length alpha through the approximation by a quadratic function. If the alpha is not sot sufficiently to the minimum a refit of the function is used.

Usage

quadraticinterpolation(phi.f, l = 0, u = 1, eps = 1e-06)

Arguments

phi.f	A univariate function.
l, u	Numbers, initial interval (or points).
eps	A number, used in the stop condition.

Value

Returns the step length alpha.

Reduction of points, interval

To reduce the interval between the three points, first evaluate the value of the function in alpha and in the poinst: lower (l), upper (u) and middle (m). After this evaluation, it is analyzed (through comparisons) at which two points the alpha is between and are chosen the next values for the refite

About the parameter phif

phif should be a univariate function that returns the value of the function at a given point.

References

1. Rao, Singiresu S.; Engineering Optimization Theory and and Practice, 4th ed., pages 273:279.

See Also

The documentation of the function univariate_f in this package.

Examples

#phi <- function(alpha) {...}
#quadraticinterpolation(phi, l = 0, u = 10, eps = 1e-4)
#quadraticinterpolation(phi, 3, 7, 1e-5)

brunasqz/NonlinearOpMethods documentation built on Oct. 27, 2019, 5:46 a.m.