com.numericalmethod.suanshu.optimization.univariate.bracketsearch

Class BracketSearch

java.lang.Object

com.numericalmethod.suanshu.optimization.univariate.bracketsearch.BracketSearch

All Implemented Interfaces:

Minimizer<C2OptimProblem,UnivariateMinimizer.Solution>, Optimizer<C2OptimProblem,UnivariateMinimizer.Solution>, UnivariateMinimizer, java.io.Serializable

Direct Known Subclasses:

Brent, Fibonacci, Golden

public abstract class BracketSearch
extends java.lang.Object
implements UnivariateMinimizer

This class provides implementation support for those univariate optimization algorithms that are based on bracketing. Examples are Bisection method, Fibonacci search, and Golden-section search. Starting with a 3-point bracketing interval of a minimum, i.e., x^l, x^a, x^u, the search iteratively reduce the length of the interval. It computes a 4th point, x^b, according to an interval dividing schedule, to form two overlapping sub-intervals, e.g., [x^l, x^a], and [x^b, x^u]. The sub-interval that contains the new minimum is chosen. Repeat the procedure until convergence. This algorithm is most effective for a uni-modal function in interval [x^l, x^u].

See Also:

"Andreas Antoniou and Wu-Sheng Lu, "Chapter 4," Practical Optimization: Algorithms and Engineering Applications. Springer.", Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected class	BracketSearch.Solution

Field Summary

Fields

Modifier and Type	Field and Description
protected double	epsilon the convergence tolerance
protected int	maxIterations the maximum number of iterations

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	BracketSearch(double epsilon, int maxIterations) Construct a univariate minimizer using a bracket search method.

Method Summary

Modifier and Type	Method and Description
UnivariateMinimizer.Solution	solve(UnivariateRealFunction f) Minimize a univariate function.

Methods inherited from class java.lang.Object

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

Methods inherited from interface com.numericalmethod.suanshu.optimization.Optimizer

solve

Field Detail

epsilon

protected final double epsilon

the convergence tolerance

maxIterations

protected final int maxIterations

the maximum number of iterations

Constructor Detail

BracketSearch

protected BracketSearch(double epsilon,
                        int maxIterations)

Construct a univariate minimizer using a bracket search method.

Parameters:

epsilon - the convergence tolerance; It should be no less than the square root of the machine precision.

maxIterations - the maximum number of iterations

Method Detail

solve

public UnivariateMinimizer.Solution solve(UnivariateRealFunction f)
                                   throws java.lang.Exception

Minimize a univariate function.

Parameters:

f - the objective function

Returns:

the minimizer

Throws:

java.lang.Exception