hs62.gms : Hock - Schittkowski Problem 62

Description

This is a popular test problem from the early 80s. The sqr term
creates problems for some solvers because the second partial
derivatives are not defined. The problems solves much better
if the sqr term is removed.

eq1.. 20*sqr(x1+x2+x3-1) =e= 0;
eq1..        x1+x2+x3-1  =e= 0;

Reference

  • Hock, W, and Schittkowski, K, Test Examples for Nonlinear Programming Codes. Springer Verlag, Lecture Notes in Economics and Mathematical Systems, 1981.

Small Model of Type : NLP


Category : GAMS Model library


Main file : hs62.gms

$title Hock - Schittkowski 1981 - Problem 62 (HS62,SEQ=264)
* This is a popular test problem from the early 80s. The sqr term
* creates problems for some solvers because the second partial
* derivatives are not defined. The problems solves much better
* if the sqr term is removed.
*
* eq1.. 20*sqr(x1+x2+x3-1) =e= 0;
* eq1..        x1+x2+x3-1  =e= 0;
*
*
*  Hock and Schittkowski, Lecture Notes in Economics and Mathematical
*  Systems, Springer Verlag, 1981.


variables obj; positive variables x1,x2,x3; equations objdef,eq1, eq1x;


objdef..  obj =e= -32.174*( 255.*log((x1+x2+x3+0.03)/(0.09*x1+x2+x3+0.03))
                          + 280.*log((x2+x3+0.03)/(0.07*x2+x3+0.03))
                          + 290.*log((x3+0.03)/(0.13*x3+0.03)));

eq1 .. 20*sqr(x1+x2+x3-1) =e= 0;
eq1x..        x1+x2+x3-1  =e= 0;

model m  / objdef, eq1  /
model mx / objdef, eq1x /;

* x1.l=1/3; x2.l=1/3; x3.l=1/3;

solve m  us nlp min obj;
* solve mx us nlp min obj;

scalar global global solution / -0.262725145e5 /
       diff   optcr - relative distance from global;

diff = (global - obj.l)/global; display global, obj.l, diff;