Consider the following unconstrained optimization problem:

Maximize f(x) 3x1x2 3x2x3  x1 2  6x2 2  x3 2

.

(a) Describe how solving this problem can be reduced to solving a two-variable unconstrained optimization problem.

D,I

(b) Starting from the initial trial solution (x1, x2, x3) (1, 1, 1), interactively apply the gradient search procedure with  0.05 to solve (approximately) the two-variable problem identified in part (a).

C

(c) Repeat part

(b) with the automatic routine for this procedure

(with  0.005).

D,I,C 13.5-8.* Starting from the initial trial solution (x1, x2) (0, 0), interactively apply the gradient search procedure with  1 to solve

(approximately) each of the following problems, and then apply the automatic routine for this procedure (with  0.01).

(a) Maximize f(x) x1x2 3x2  x1 2  x2 2

.

(b) Minimize f(x) x1 2

x2 2 2x1 2 2x2 2  4x1 4x2.