Use SUMT to solve the following convex programming problem:

Minimize f(x)

(x1 3

1)3 x2, subject to x1  1 and x2  0.

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

(b) Derive the minimizing 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) (2, 1), use the automatic routine in your OR Courseware to apply SUMT to this problem (in maximization form) with r 1, 102 , 104 , 106 .