ContinuousOptimizationMaximizeTFunctionParameter(FuncDoubleMatrix, TFunctionParameter, Double, DoubleMatrix, TFunctionParameter) Method

Finds the maximum of the specified parametric objective function.

Definition

Namespace: Novacta.Analytics
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a

C#

public static DoubleMatrix Maximize<TFunctionParameter>(
	Func<DoubleMatrix, TFunctionParameter, double> objectiveFunction,
	DoubleMatrix initialArgument,
	TFunctionParameter functionParameter
)

VB

Public Shared Function Maximize(Of TFunctionParameter) ( 
	objectiveFunction As Func(Of DoubleMatrix, TFunctionParameter, Double),
	initialArgument As DoubleMatrix,
	functionParameter As TFunctionParameter
) As DoubleMatrix

C++

public:
generic<typename TFunctionParameter>
static DoubleMatrix^ Maximize(
	Func<DoubleMatrix^, TFunctionParameter, double>^ objectiveFunction, 
	DoubleMatrix^ initialArgument, 
	TFunctionParameter functionParameter
)

F#

static member Maximize : 
        objectiveFunction : Func<DoubleMatrix, 'TFunctionParameter, float> * 
        initialArgument : DoubleMatrix * 
        functionParameter : 'TFunctionParameter -> DoubleMatrix

Parameters

objectiveFunction FuncDoubleMatrix, TFunctionParameter, Double: The objective function to be maximized.
initialArgument DoubleMatrix: The argument at which the method starts the search for optimality.
functionParameter TFunctionParameter: The function parameter.

Type Parameters

TFunctionParameter: The type of the function parameter.

Return Value

DoubleMatrix
The argument at which the function is maximized.

Remarks

It is assumed that the objectiveFunction will accept row vectors as valid representations of an argument. As a consequence, initialArgument is expected to be a row vector.

Example

In the following example, function

LaTeX equation

is maximized.

The search for the maximizer starts from the initial argument LaTeX equation .

Maximizing a parametric function.

using System;

namespace Novacta.Analytics.CodeExamples
{
    public class ContinuousOptimizationExample1  
    {
        public void Main()
        {
            // Define the parametric objective function as follows: 
            // f(x, a) = exp(-(x-2)^2) + (a) * exp(-(x+2)^2)).
            static double objectiveFunction(DoubleMatrix x, double alpha)
            {
                double y = 0.0;
                var x_0 = x[0];
                y += Math.Exp(-Math.Pow(x_0 - 2.0, 2.0));
                y += alpha * Math.Exp(-Math.Pow(x_0 + 2.0, 2.0));

                return y;
            }

            // Define the argument at which the method starts 
            // the search for optimality.
            var initialArgument = DoubleMatrix.Dense(1, 1, -6.0);

            // Define the function parameter.
            double functionParameter = .8;

            // Maximize the objective function.
            var maximizer = ContinuousOptimization.Maximize(
                objectiveFunction: objectiveFunction,
                initialArgument: initialArgument,
                functionParameter: functionParameter);

            // Show the results.
            Console.WriteLine();
            Console.WriteLine("The maximizer of the objective function is:");
            Console.WriteLine(maximizer);

            Console.WriteLine();

            Console.WriteLine("The maximum value of the objective function is:");
            Console.WriteLine(objectiveFunction(maximizer, functionParameter));
        }
    }
}

// Executing method Main() produces the following output:
// 
// 
// The maximizer of the objective function is:
// 2.00000529       
// 
// 
// 
// The maximum value of the objective function is:
// 1.0000000899963821

Exceptions

ArgumentNullException	objectiveFunction is null. -or- initialArgument is null.
ArgumentException	initialArgument is not a row vector.