1 /*

2

3 Curve fitting problem 12.11(a) H P Williams "Model Building in Mathematical Programming"

4

5 Dr. H J Mackenzie

6 HARD software

7 hjm@hardsoftware.com

8

9 2006-01-05

10

11 */

12

13 # set of points

14

15 set I;

16

17 # independent variable

18

19 param x {i in I};

20

21 # dependent variable

22

23 param y {i in I};

24

25 # output input values

26

27 printf {i in I} "x = %.1f; y = %.1f\n", x[i], y[i];

28

29 # define equation variables

30

31 var a;

32

33 var b;

34

35 var u {i in I}, >= 0;

36

37 var v {i in I}, >= 0;

38

39 # define objective function

40

41 minimize error: sum {i in I} u[i] + sum {i in I} v[i];

42

43 # define equation constraint

44

45 s.t. equation {i in I} : b * x[i] + a + u[i] - v[i] = y[i];

46

47 solve;

48

49 printf "y = %.4fx + %.4f\n", b, a;

50

51 /*

52 *

53 * DATA section

54 *

55 */

56

57 data;

58

59 param : I : x y :=

60 1 0 1

61 2 0.5 0.9

62 3 1 0.7

63 4 1.5 1.5

64 5 1.9 2

65 6 2.5 2.4

66 7 3 3.2

67 8 3.5 2

68 9 4 2.7

69 10 4.5 3.5

70 11 5 1

71 12 5.5 4

72 13 6 3.6

73 14 6.6 2.7

74 15 7 5.7

75 16 7.6 4.6

76 17 8.5 6

77 18 9 6.8

78 19 10 7.3

79 ;

80

81 end;