1.1 De Jong's function 1	Contents	1.3 Rotated hyper-ellipsoid function

1 Parametric Optimization

1.2 Axis parallel hyper-ellipsoid function

The axis parallel hyper-ellipsoid is similar to De Jong's function 1. It is also known as the weighted sphere model. Again, it is continuos, convex and unimodal.

function definition

f1a(x)=sum(i·x(i)^2), i=1:n;
-5.12<=x(i)<=5.12.

global minimum

f(x)=0; x(i)= 0, i=1:n.

This function is implemented in objfun1a.

Moved axis parallel hyper-ellipsoid function

This function is derived from the axis parallel hyper-ellipsoid. There is a slight difference between these two function definitions. In the end the moved axis parallel hyper-ellipsoid function is more elliptic than the original function and the minimum of the function is not at x(i) = 0.

function definition

f1c(x)=sum(5*i·x(i)^2), i=1:n;
-5.12<=x(i)<=5.12.

global minimum

f(x)=0; x(i)= 5*i, i=1:n.

This function is implemented in objfun1c.

The figure below shows the mesh plot of the first and fourth variable. The objective values were calculated from the 4-dimensional function with second and third variable set to 0.