# Question

Consider the following nonconvex programming problem:

Minimize f (x) = sin 3x1 + cos 3x2 + sin(x1 + x2),

subject to

x12 – 10x2 ≥ – 1

10x1 + x22 ≤ 100 and

x1 ≥ 0, x2 ≥ 0.

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

(b) Describe how SUMT should be applied to attempt to obtain a global minimum. (Do not actually solve.)

(c) Use the global optimizer feature of LINGO to solve this problem.

(d) Use MPL and its global optimizer LGO to solve this problem.

Minimize f (x) = sin 3x1 + cos 3x2 + sin(x1 + x2),

subject to

x12 – 10x2 ≥ – 1

10x1 + x22 ≤ 100 and

x1 ≥ 0, x2 ≥ 0.

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

(b) Describe how SUMT should be applied to attempt to obtain a global minimum. (Do not actually solve.)

(c) Use the global optimizer feature of LINGO to solve this problem.

(d) Use MPL and its global optimizer LGO to solve this problem.

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