UniDimensionalSolver.SeekExtremeUnidir Method

Evaluates the location of a (local) extremum (i.e. maximum or minimum) of the unidimensional object function, where the specific bracketing and locate algorithms from the classs BracketingAlgorithm and LocateAlgorithm are set and the initial point given.

public Extremum SeekExtremeUnidir(
   double initialPoint,
   BracketingAlgorithm bracketingAlgorithm,
   LocateAlgorithm locateAlgorithm,
   double minDistance,
   double bracketingParameter,
   double tolerance,
   int maxIterations
);

Parameters

initialPoint: The initial point for which the iterative search from the extremum is started from.
bracketingAlgorithm: The bracketing algorithm used selected from the class BracketingAlgorithm.
locateAlgorithm: The locate algorithm used selected from the class LocateAlgorithm.
minDistance: This parameter is required by all bracketing algorithms within BracketingAlgorithm, and usually signifies the minimal distance between the end points of any bracketed interval in which the extremum lies. Therefore, the minDistance parameter should be approximately the same magnitude as tolerance parameter.
bracketingParameter: This parameter is required by some bracketing algorithms. For a detailed explanation as to its meaning and use for particular bracketing algorithms selected please see the BracketingAlgorithm documentation or the Mathematical Documentation chapter of the accompanying PDF documentation.
tolerance: The tolerance used within the exit condition of the iterative locate algorithm used. A reasonable value to take for the tolerance is 1E-5.
maxIterations: The maximum number of iterations used only in the iterative locate algorithms, in such cases a reasonable value to use is 300. If the number of iterations exceeds this number TooManyUniDimensionalIterationsException will be thrown.

Return Value

an object containing the point where the function has a local extremum greater than initialPoint and the type of that extremum (-1 when we have a maximum; 1 when we have a minimum

Remarks

This method returns the type Extremum which contains the coordinate value of the extremum sought of the type of extremum found (i.e. whether maximum or minimum). In order to find the value of the object function at the extremum found you may use SeekExtremeValueUnidir, which applied the same algorithm except but returns the value of the object function at the extremum rather than the coordinate value of the extremum found.

Remark: This approach in general will yield less precise results than SeekExtremeBidir, for corresponding choices of the locate and bracketing algorithms, but will also also be faster by a factor of two.

Application of this Approach

Before this method is called the uni-dimensional object function of the optimization problem must be set (i.e. provided for the method) using either {@link #setFunction}, or passed using the constructor during the instantiation of the instance of the UniDimensionalSolver class. For further details, detailing exactly how the object function is implemented and then send to an instance of this class we refer the reader to SetFunction documentation. In is true that most users will find the {@link #setFunction} approach to be more user friendly, however it should be pointed out that if your application uses threads then this approach is not thread safe.

Once the object function has been set you should specify the specific bracketing and locate algorithms which are used within this method, by passing as parameters the appropriate procedure from the classs BracketingAlgorithm and LocateAlgorithm.

The iterative search will begin from the point initialPoint, with the accuracy of the result depending on the algorithms chosen and the algorithms settings corresponding to the last four parameters. The last four parameters do not have a general interpretation but there exact meaning and use should become clear once the bracketing and location algorithms are chosen and we refer the read to the corresponding documentation of the classs BracketingAlgorithm and LocateAlgorithm, or the Mathematical Documentation chapter of the PDF documentation for further details.

Exceptions