Introduction to Unconstrained Optimization - Scilab

2.0
1.5
1.0
100
0.5
500
10
500
0.0
1e+003
2
10
-0.5
2e+003
100
-1.0
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Figure 3: Contours of Rosenbrock’s function.
whatever the choice of x : this is because the exp function is so that e x → 0 as
x → −∞.
Let us plot several level sets of Rosenbrock’s function. To do so, we can use the
contour function. One small issue is that the contour function expects a function
which takes two variables x1 and x2 as input arguments. In order to pass to contour
a function with the expected header, we define the rosenbrockC function, which
takes the two separate variables x1 and x2 as input arguments. Then, it gathers the
two parameters into one column vector and delegates the work to the rosenbrock
function.
function f = rosenbrockC ( x1 , x2 )
f = rosenbrock ( [x1 ,x2]’ )
endfunction
We can finally call the contour function and draw various level sets of Rosenbrock’s
function.
x1 = linspace ( -2 , 2 , 100 );
x2 = linspace ( -1 , 2 , 100 );
contour (x1 , x2 , rosenbrockC , [2 10 100 500 1000 2000] )
This produces the figure 3.
We can also create a 3D plot of Rosenbrock’s function. In order to use the surf
function, we must define the auxiliary function rosenbrockS, which takes vectors of
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