May 2015
Intermediate to advanced
466 pages
10h 33m
English
Content preview from Optimization
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189Constrained Optimization
The optimization problem is
Minimize
f x x x x x x x( ) . . . .x = + + +0 6224 1 7781 3 1661 19 84
1 3 4 2 3
2
1
2
4
xx x
1
2
3
subject to
g
1
(x) = −x
1
+ 0.0193x
3
≤ 0
g
2
(x) = −x
2
+ 0.00954x
3
≤ 0
g x x x
3 3
2
4 3
3
4
3
1 296 000 0( ) , ,x = − − + ≤π π
g
4
(x) = x
4
− 240 ≤ 0
where
0 ≤ x
1
, x
2
≤ 10, 10 ≤ x
3
, x
4
≤ 200
Solve the constrained optimization problem using the SQP method
with an initial guess of (4, 4, 100, 100).
On executing the SQP code, the function minimum obtained is
5885.3407 and occurs at (0.7782, 0.3848, 40.3196, 200). The convergence
history is shown in the following table.
No. x-vector
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