Page 332 - MATLAB an introduction with applications

Optimization ——— 317

P5.6: Find the minimum of the following function using Powell’s method:

2
2
() =
Fx 7x + 5x − 8x x − 5x 1
1
2
1 2
Starting from (0, 0).
P5.7: Repeat Problem P5.5 using Fletcher-Reeves method.
P5.8: Repeat Problem P5.6 using Fletcher-Reeves method.
2
2
P5.9: Minimize f(x , x ) = x – x + 2x + 2x x + x starting from the point (0, 0) using Hook and Jeeves
1
2
2
1
1
1 2
2
method.
P5.10: Repeat Problem P5.1 using Hooke and Jeeves method.
2
P5.11: Minimize f(x , x ) = (x – 1) + (x – 1) 2
1
1
2
2
subject to g (x , x ) = –x ≤ 0
1
1
2
1
g (x , x ) = –x ≤ 0
2
2
1
2
2
2
g (x , x ) = x + x – 1 ≤ 0
1
2
3
2
1
2 x 2
P5.12: Minimize f(x , x ) = (x – 1) + 2
1
2
1
subject to g (x , x ) = –x ≤ 0
1
2
2
2
2
g (x , x ) = x – (1 – x ) ≤ 0
2
2
1
1
3
P5.13: Use the MATLAB fminbnd function to find the minimum of the function in Problem P5.9.
2
2
P5.14: Minimize f(x , x ) = 90(x – x ) + (1 – x ) using the starting point (x = –1.1, x = 1.0). Use MATLAB
2
1
1
2
2
1
1
built-in function fminsearch.
P5.15:
4
2
(a) Minimize (x – x ) + (x – x ) .
3
2
2
1
Initial guess: (–2.5, 2, 2)
(b) Minimize x x (x + x + x ) + x 3
3
1 4
2
1
Initial guess: (1, 4, 5, 1).
P5.16:
Minimize x + 2x + 3x + exp(x x )
1 4
3
1
2
Initial guess: (1, 2, 1, 2).
P5.17:
Minimize f(x) = x + 54x + 3x 3
1
2
subject to x + 5x – x ≥ 4
1
2
3
–x + x + 2x ≥ 1
3
1
2
–x + 3x + 3x ≥ 5
3
2
1
–3x + 8x – 5x ≥ 3
2
1
3
0
Initial guess: x = (0, 1, 1).
P5.18:
Minimize f (x) = x + 5x 2
1