ComputeObjectiveFunction

Myriad objective function for specific sample and parameters.

Contents

Syntax.

[ Q_of_theta, theta ] = ComputeObjectiveFunction( X );
[ Q_of_theta, theta ] = ComputeObjectiveFunction( X , ...);

Definitions.

For $\gamma \in R$, $w=(w_1, \dots, w_n) \in R^n$ and $X=(x_1, \dots, x_n) \in R^n$ the objective function is defined by

$$f(\theta) = \sum_{i=1}^n \log(\gamma ^2 + w_i (x_i - \theta)^2)$$

Description.

[ Q_of_theta, theta ] = ComputeObjectiveFunction( X ) computes the objective function for a sample vector X.

Example.

% Define gamma parameter
gamma=0.03;

% Create a sample vector.
X= [0.13, 0.86, 0.39, 0.99, 0.27, 0.95, 0.97, 0.16, 0.90];

% Create a weights  vector.
w= [0.70, 0.36, 0.94, 0.22, 0.39, 0.04, 0.26, 0.60, 0.02];

% Compute the objective function.
[ Q_of_theta, theta ] = ComputeObjectiveFunction( X ,...
                                                     'Weights', w,...
                                                     'Gamma', gamma);

% Display the objective function.
figure, plot(theta, Q_of_theta), title('Objective function.')

Input arguments.

Example : [ Q_of_theta, theta ] = ComputeObjectiveFunction( X , 'Theta', linspace(0,1,50));