$TITLE NLP Example (simple) 1
$OFFUPPER
*
*
* Ref:  From C&O666 notes and from Borwein's notes
*
*---------------------------------------------------------------------

 SETS     J         index      / J1 * J2 / ;

 VARIABLES
      X(J)   unknowns
      Z      optimal value  ;

X.LO('J1') = 0 ;

 EQUATIONS 
    COST   define objective function
    CONSTR1 single constraint linear 
    CONSTR2 single constraint linear ;
 
 COST..  Z =E= SQR(X('J1')) + SQR(X('J2')) ;
 CONSTR1 .. X('J1') + X('J2') =E= 1 ;
 CONSTR2 .. X('J1') + X('J2') =E= 2 ;

MODEL NLP1 /ALL/;

 SOLVE NLP1  MINIMIZING Z USING NLP;