/*

   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;