alpar@9: /*
alpar@9: 
alpar@9:   Curve fitting problem 12.11(b) H P Williams "Model Building in Mathematical Programming"
alpar@9: 
alpar@9:   Dr. H J Mackenzie
alpar@9:   HARD software
alpar@9:   hjm@hardsoftware.com
alpar@9: 
alpar@9:   2006-01-23
alpar@9: 
alpar@9:  */
alpar@9: 
alpar@9: # set of points
alpar@9: 
alpar@9: set I;
alpar@9: 
alpar@9: # independent variable
alpar@9: 
alpar@9: param x {i in I};
alpar@9: 
alpar@9: # dependent variable
alpar@9: 
alpar@9: param y {i in I};
alpar@9: 
alpar@9: # output input values
alpar@9: 
alpar@9: printf {i in I} "x = %.1f; y = %.1f\n", x[i], y[i];
alpar@9: 
alpar@9: # define equation variables
alpar@9: 
alpar@9: var a;
alpar@9: 
alpar@9: var b;
alpar@9: 
alpar@9: var u {i in I}, >= 0;
alpar@9: 
alpar@9: var v {i in I}, >= 0;
alpar@9: 
alpar@9: var z;
alpar@9: 
alpar@9: # define objective function
alpar@9: 
alpar@9: minimize deviation: z;
alpar@9: 
alpar@9: # define equation constraint
alpar@9: 
alpar@9: s.t. equation {i in I} : b * x[i] + a + u[i] - v[i] = y[i];
alpar@9: 
alpar@9: # define deviation constrains
alpar@9: 
alpar@9: s.t. u_deviation {i in I} : z - u[i] >= 0;
alpar@9: s.t. v_deviation {i in I} : z - v[i] >= 0;
alpar@9: 
alpar@9: solve;
alpar@9: 
alpar@9: printf "y = %.4fx + %.4f Max deviation = %.4f\n", b, a, z;
alpar@9: 
alpar@9: /*
alpar@9:  *
alpar@9:  * DATA section
alpar@9:  *
alpar@9:  */
alpar@9: 
alpar@9: data;
alpar@9: 
alpar@9: param : I :   x    y :=
alpar@9:         1     0    1
alpar@9:         2   0.5  0.9
alpar@9:         3     1  0.7
alpar@9:         4   1.5  1.5
alpar@9:         5   1.9    2
alpar@9:         6   2.5  2.4
alpar@9:         7     3  3.2
alpar@9:         8   3.5    2
alpar@9:         9     4  2.7
alpar@9:        10   4.5  3.5
alpar@9:        11     5    1
alpar@9:        12   5.5    4
alpar@9:        13     6  3.6
alpar@9:        14   6.6  2.7
alpar@9:        15     7  5.7
alpar@9:        16   7.6  4.6
alpar@9:        17   8.5    6
alpar@9:        18     9  6.8
alpar@9:        19    10  7.3
alpar@9: ;
alpar@9: 
alpar@9: end;