Page 333 - MATLAB an introduction with applications

318 ——— MATLAB: An Introduction with Applications

subject to x + x ≤ 3
1
2
–x + x ≤ 1.5
2
1
0
Initial guess: x = (–1, 1).
P5.19: Solve Problem P5.17 with x , x , x ≥ 0.
3
2
1
P5.20: Solve Problem P5.18 with x , x ≥ 0.
2
1
P5.21:
2 2
Minimize f (x) = 100(x – x ) + (1 – x ) 2
2
1
1
subject to x + 1 ≥ 0
1
1 – x ≥ 0
2
5x – x – 1 ≥ 0
2
1
2 – x – 2x ≥ 0
1
2
Initial guess: [–1, 1].
P5.22:
2
2
Minimize f(x) = x + x + x 3 2
2
1
subject to 1 – x x ≥ 0
2 3
x – x ≥ 0
3
1
2
x – x + x x – 5 = 0
1
2 3
2
0 ≤ x ≤ 5
1
0 ≤ x ≤ 3
2
0 ≤ x ≤ 4
3
Initial guess: [–1, 1].
P5.23:
Minimize f(x) = 2x – 3(x – 4) 2
2
1
2
subject to x + x 2 2 –10 ≤ 0
1
x + (x 2 – 4) ≤ 0
4
2
1
Initial guess: [–1, 1].
P5.24:
Minimize f (x) = (x – x ) + x 2
2
2
1
subject to 1 – x + x ≤ 1
2
1
x + 2x ≤ 4
2
1
x ≥ 0
1
x ≥ 0
2
Initial guess: [2, 0].
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