Consider the following unconstrained optimization problem:

Maximize f(x)
2x1x2  x2  x1 2  2x2 2

.

D,I

(a) Starting from the initial trial solution (x1, x2)
(1, 1), interactively apply the gradient search procedure with 
0.25 to obtain an approximate solution.

(b) Solve the system of linear equations obtained by setting

f(x)
0 to obtain the exact solution.

(c) Referring to Fig 12.14 as a sample for a similar problem, draw the path of trial solutions you obtained in part (a). Then show the apparent continuation of this path with your best guess for the next three trial solutions [based on the pattern in part

(a) and in Fig. 12.14]. Also show the exact solution from part

(b) toward which this sequence of trial solutions is converging.

C

(d) Apply the automatic routine for the gradient search procedure (with 
0.01) in your IOR Tutorial to this problem.