The Steepest Descent Algorithm for Unconstrained Optimization and ...

10
8
6
4
2
0
−2
−5 0 5
Figure 2: Behavior of the steepest descent algorithm for the example of
Subsection 4.1.
A
For this problem, a
=30.234, and so the linear convergence rate δ of
(
A/a−1 ) 2
the steepest descent algorithm is bounded above by δ =
A/a+1
=0.8760.
If we apply the steepest descent algorithm to minimize f (x) starting
from x 1 =(40, −100), we obtain the iteration values shown in Table 3 and
shown graphically in Figure 3.
4.3 Example 3: Rapid Convergence
Consider the function
f (x) = 1 x T Qx − c T x +10
2
11