Exercise Solution 2.21
Details of this solution are available as an Excel spreadsheet.
The Jacobian of f is:
Based upon this, we apply Newton’s method with line searches. Results are indicated below.
Exhibit s1: The process converges rapidly.
A line search was used to obtain x. Newton’s method originally determined x = (1.7515, 1.7636), which failed criterion [2.153]. Applying a line search, yielded λ* = 0.1533. This corresponded to value x* = (1.9619, 0.5525). We set x = x*. This did satisfy criterion [2.153]. No other line searches were required.