com.numericalmethod.suanshu.optimization.univariate
Class Golden

java.lang.Object
  com.numericalmethod.suanshu.optimization.univariate.BracketSearch
      com.numericalmethod.suanshu.optimization.univariate.Golden

public class Golden
extends BracketSearch

Minimum finding algorithm by the golden section.

On each iteration, the algorithm compares the distances to the lower and upper ends of the bracketing interval. The bigger sub-interval is divided by the golden section (about 0.3189660...) by the next point. The value of the function at this new point is calculated and compared to the current minimum. A new bracketing interval is then chosen in the usual manner as in BracketSearch.

Choosing the golden section as the bisection ratio gives the fastest convergence among the algorithms that converge linearly.

This implementation is much simpler than that of Fibonacci. It does not run the risk that the next guess lies outside the bracketing interval.

Field Summary

Fields inherited from class com.numericalmethod.suanshu.optimization.univariate.BracketSearch

f, tol

Constructor Summary

Golden()

Method Summary

double

search(int maxIterations, double lower, double upper) Search for a minimum within the interval [lower, upper].

Methods inherited from class com.numericalmethod.suanshu.optimization.univariate.BracketSearch

minimum, search, solve

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Golden

public Golden()

Method Detail

search

public double search(int maxIterations,
                     double lower,
                     double upper)

Search for a minimum within the interval [lower, upper].

Parameters:

maxIterations - number of iterations

lower - lower bound for the bracketing interval which contains a minimum

upper - upper bound for the bracketing interval which contains a minimum

Returns:

an approximate minimizer