least.gms : Nonlinear Regression Problem

Description

Nonlinear least squares estimation problem of Mitcherlisch's law.

Reference

  • Bracken, J, and McCormick, G P, Chapter 8.4. In Selected Applications of Nonlinear Programming. John Wiley and Sons, New York, 1968, pp. 89-90.

Small Model of Type : NLP


Category : GAMS Model library


Main file : least.gms

$title Nonlinear Regression Problem   (LEAST,SEQ=24)
$Ontext

Nonlinear least squares estimation problem of Mitcherlisch's law.


Bracken, J, and McCormick, G P, Chapter 8.4. In Selected Applications of
Nonlinear Programming. John Wiley and Sons, New York, 1968, pp. 89-90.

$Offtext

set i  observation number / 1*6 /

     table dat(i,*)  basic data

    y       x
1  127     -5
2  151     -3
3  379     -1
4  421      5
5  460      3
6  426      1

variables ols  ordinary least squares
          dev(i) deviation
          b1, b2, b3

equations dols    definition of ols
          ddev(i) definition of deviations
          sequ    single equation definition ;

dols..    ols =e= sum(i, sqr(dev(i)));

ddev(i).. dat(i,"y") =e= b1 + b2*exp(b3*dat(i,"x")) + dev(i);

sequ..    ols =e= sum(i, sqr(dat(i,"y")-b1-b2*exp(b3*dat(i,"x"))));

model least  ordinary least squares / dols, ddev /
      single single equ definition  / sequ / ;

b1.l = 500; b2.l = -150; b3.lo = -5.0;
                         b3.l  = - .2;
                         b3.up =  5.0;

solve single minimizing ols using nlp;

solve least minimizing ols using nlp;