$ondollar title Custom Computer (NLP) Example 13.2 of Rardin (1998)

$offsymxref offsymlist offuelxref offuellist offupper
option limrow = 0, limcol = 0;

set i "data points" /1*12/;

parameter p(i) "number of units of point i"
/1 19, 2 2, 3 9, 4 4, 5 5, 6 6, 7 3, 8 11, 9 14, 10 17, 11 1, 12 20/;

parameter q(i) "order cost of point i"
/1 7.9, 2 25.0, 3 13.1, 4 17.4, 5 19.5, 6 13.0,
7 17.8, 8 8.0, 9 9.2, 10 6.3, 11 42.0, 12 6.6/;

free variables
sqresid  "total squared residuals",
x1   "linear parameter of the regression model",
x2   "exponential parameter of the regression model";

equation
obj  "minimize total squared residuals";

obj..
sqresid =e= sum(i, sqr(q(i) - x1*p(i)**x2) );

model custcomp /all/;

x1.l = 32.00;
x2.l = -0.40;

solve custcomp using nlp minimizing sqresid;