TMtxOptimization Class

type TMtxOptimization = class(TMtxComponent);

Interfaces the optimization routines.

The component can be used to find the minimum of function of several variables.

How to use TMtxOptimization component?

Drop a TMtxOptimization component on the form.
Define the number of variables and their initial values by accessing the TMtxOptimization.VariableParameters vector.
Define any additional constant parameters by accessing TMtxOptimization.ConstantParameters vector.
Define any additional constant pointer parameter by using the TMtxOptimization.SetObjects method.
Define real function (must be of TRealFunction type).
Define optimization method by accessing the TMtxOptimization.OptimizationMethod property.
Depending on optimization method you'll have to (optionally) define the gradient calculation procedure (TMtxOptimization.GradProcedure method) or gradient/Hessian matrix calculation procedure (TMtxOptimization.GradHessProcedure method). If you don't specify the GradProcedure or GradHessProcedure then the numeric approximation will be used to calculate the gradient vector and Hessian matrix. In this case you must also specify which gradient aproximation method you will use - access the TMtxOptimization.NumericGradMethod property.
Call the TMtxOptimization.Recalculate method to find the minimum of function of several variables.

Results:

TMtxOptimization.MinValue : RealFunction, evaluated at minimum.
TMtxOptimization.VariableParameters : minimum position.
TMtxOptimization.Iterations: Number of iterations needed to reach specified (TMtxOptimization.Tolerance property) minimum precision.
TMtxOptimization.InverseHess : Inverse Hessian matrix (returned only by BFGS, ConjGrad and Marquardt methods)
TMtxOptimization.StopReason: Why did the optimization algorithm stopped ?

Examples

delphi

Uses Math387, MtxVecTools;

// define the real function to be minimized
function BananaFunction(const Pars: TVec; const Consts: TVec; const PConsts: Array of TObject): double;
begin
    BananaFunction := 100*Sqr(Pars[1]-Sqr(Pars[0]))+Sqr(1-Pars[0]);
end;

procedure Example(MtxOptim: TMtxOptimization);
begin
    if Assigned(MtxOptim) then
begin
    // define two variables and their initial values
    MtxOptim.VariableParameters.SetIt(false,[2,-1]);
    // use BFGS optimization method
    MtxOptim.OptimizationMethod := optBFGS;
    // tolerance for MinValue and gradient calculation
    // additional note : since we did not define the GradProc,
    // the internal numerical gradient approximation will be used
    MtxOptim.Tolerance := 2.0e-6;
    MtxOptim.GradTolerance := 2.0e-6;
    // function to be minimized
    MtxOptim.RealFunction := BananaFunction;
    // finally, calculate minimum
    MtxOptim.Recalculate;
end;
end;

Properties

Name	Type	Description
AutoUpdate	Boolean	Automatic recalculation.
BlockAssign	Boolean	Block streaming of specific properties when storing only a "template".
ConstantParameters	TVec	set/read the additional constants used in minimized function.
Dirty	Boolean	Becomes true after any of the properties have changed.
EditorActive	Boolean	Returns True, if the component editor is displayed.
GradHessProcedure	TGradHess	Defines the gradient vector and Hessian matrix calculation routine.
GradProcedure	TGrad	Defines the gradient vector calculation routine.
GradTolerance	Double	The precision for numeric gradient and/or Hessian matrix calculation.
Lambda0	Double	Initial lambda step used in Marquardt optimization algorithm.
MaxIterations	Integer	maximum number of iterations allowed for minimum search.
NumericGradMethod	TNumericGradMethod	Defines which gradient numerical approximation method will be used to to evaluate gradient.
OptimizationMethod	TOptMethod	Optimization algorithm used for minimum search.
RealFunction	TRealFunction	Defines the function to be minimized.
Reference	TReferenceList	Stores a list of components that have to be notified, when this component is destroyed.
SoftSearch	Boolean	Internal line search algorithm.
StopReason	TOptStopReason	Stop reason for optimization algorithm.
Tolerance	Double	Precision.
VariableParameters	TVec	Set/read the variables in minimized function.
Verbose	TStrings	If not nil then the optimization method uses it for logging each optimization step.

Methods

Name	Description
AllowStreaming	Returns the negatated value of BlockAssign.
Assign	Assign values of all published properties from Source.
AssignTemplate	Assign values of "template-like" published properties from Source.
EditorClass	To be overriden in descendanr classses.
LoadFromStream	Load the component from Src stream.
LoadTemplateFromFile	Load a template from file.
LoadTemplateFromStream	Load a template from stream.
Recalculate	Triggers TMtxOptimization recalculation.
Reset	Reset is called after loading the data from stream or file.
SaveTemplateToFile	Save template to file.
SaveTemplateToStream	Save template to stream.
SaveToStream	Save the component to Dst stream.
SetObjects	Define any additional Object constant parameters in the RealFunction.