blob: 56f1ba10697f80fba1136be15e275a19dc45318d (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
|
/*
Curve fitting problem 12.11(b) H P Williams "Model Building in Mathematical Programming"
Dr. H J Mackenzie
HARD software
hjm@hardsoftware.com
2006-01-23
*/
# set of points
set I;
# independent variable
param x {i in I};
# dependent variable
param y {i in I};
# output input values
printf {i in I} "x = %.1f; y = %.1f\n", x[i], y[i];
# define equation variables
var a;
var b;
var u {i in I}, >= 0;
var v {i in I}, >= 0;
var z;
# define objective function
minimize deviation: z;
# define equation constraint
s.t. equation {i in I} : b * x[i] + a + u[i] - v[i] = y[i];
# define deviation constrains
s.t. u_deviation {i in I} : z - u[i] >= 0;
s.t. v_deviation {i in I} : z - v[i] >= 0;
solve;
printf "y = %.4fx + %.4f Max deviation = %.4f\n", b, a, z;
/*
*
* DATA section
*
*/
data;
param : I : x y :=
1 0 1
2 0.5 0.9
3 1 0.7
4 1.5 1.5
5 1.9 2
6 2.5 2.4
7 3 3.2
8 3.5 2
9 4 2.7
10 4.5 3.5
11 5 1
12 5.5 4
13 6 3.6
14 6.6 2.7
15 7 5.7
16 7.6 4.6
17 8.5 6
18 9 6.8
19 10 7.3
;
end;
|
