Introduction to Unconstrained Optimization - Scilab

3000
2500
2000
Z
1500
1000
500
0
2.0
1.5
1.0
0.5
Y 0.5
0.0
0.0
-0.5 X
-0.5 -1.0
-1.5
-1.0 -2.0
1.0
1.5
2.0
Figure 4: Three dimensionnal plot of Rosenbrock’s function.
data as input arguments.
function f = rosenbrockS ( x1 , x2 )
f = rosenbrock ( [ x1 x2 ] )
endfunction
The following statements allows to produce the plot presented in figure 4. Notice
that we must transpose the output of feval in order to feed surf.
x = linspace ( -2 , 2 , 20 );
y = linspace ( -1 , 2 , 20 );
Z = feval ( x , y , rosenbrockS );
surf (x,y,Z ’)
h = gcf ();
cmap = graycolormap (10);
h. color_map = cmap ;
On one hand, the 3D plot seems to be more informative than the contour plot.
On the other hand, we see that the level sets of the contour plot follow the curve
quadratic curve x 2 = x 2 1, as expected from the function definition. The surface has
the shape of a valley, which minimum is at x ⋆ = (1, 1) T . The whole picture has the
form of a banana, which explains why some demonstrations of this test case present
it as the banana function. As a matter of fact, the contour plot is often much more
simple to analyze than a 3d surface plot. This is the reason why it is used more
11