Consider the example for applying SUMT given in Sec.

13.10.

(a) Show that (x1, x2) (1, 2) satisfies the KKT conditions.

(b) Display the feasible region graphically, and then plot the locus of points x1x2 2 to demonstrate that (x1, x2) (1, 2) with f(1, 2) 2 is, in fact, a global maximum.

13.10-5.* Consider the following convex programming problem:

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

, subject to x1  3 and x2  3.

(a) If SUMT were applied to this problem, what would be the unconstrained function P(x; r) to be maximized at each iteration?

(b) Derive the maximizing solution of P(x; r) analytically, and then give this solution for r 1, 102

, 104

, 106

.

D,C

(c) Beginning with the initial trial solution (x1, x2) (4, 4), use the automatic routine in your OR Courseware to apply SUMT to this problem with r 1, 102

, 104

, 106

.