* AMPL Model by Hande Y. Benson
*
* Copyright (C) 2001 Princeton University
* All Rights Reserved
*
* Permission to use, copy, modify, and distribute this software and
* its documentation for any purpose and without fee is hereby
* granted, provided that the above copyright notice appear in all
* copies and that the copyright notice and this
* permission notice appear in all supporting documentation.

*   Source:
*   M. Palmer, Edinburgh, private communication.

*   SIF input: Nick Gould, 1990.

*   classification SBR2-RN-4-0

$Set M 23
Set I              /i1*i%M%/;

Parameter X[i]  / i1   -1.658063  ,  i2   -1.570796  ,  i3   -1.396263  ,
                  i4   -1.221730  ,  i5   -1.047198  ,  i6   -0.872665  ,
                  i7   -0.741119  ,  i8   -0.698132  ,  i9   -0.523599  ,
                 i10   -0.349066  , i11   -0.174533  , i12    0.0       ,
                 i13    0.174533  , i14    0.349066  , i15    0.523599  ,
                 i16    0.698132  , i17    0.741119  , i18    0.872665  ,
                 i19    1.047198  , i20    1.221730  , i21    1.396263  ,
                 i22    1.570796  , i23    1.658063  /  ;

Parameter Y[i]  / i1   67.27625   ,  i2  52.8537     ,  i3  30.2718     ,
                  i4   14.9888    ,  i5   5.5675     ,  i6   0.92603    ,
                  i7    0.0       ,  i8   0.085108   ,  i9   1.867422   ,
                 i10   5.014768   , i11   8.263520   , i12   9.8046208  ,
                 i13   8.263520   , i14   5.014768   , i15   1.867422   ,
                 i16   0.085108   , i17   0.0        , i18   0.92603    ,
                 i19   5.5675     , i20  14.9888     , i21  30.2718     ,
                 i22  52.8537     , i23  67.27625    /  ;

Positive Variable B , C , D

         Variable A , palmer ;

Equation Def_obj ;

Def_obj..  palmer =e=sum{i,sqr(Y[i] -(A*sqr(X[i]) +( B/(C +sqr(X[i])/D ))))};

A.l = 1.0 ;
B.l = 1.0 ;
C.l = 1.0 ;
D.l = 1.0 ;

Model palmer4  /all/;

solve palmer4  using nlp minimazing  palmer;

display A.l , B.l , C.l , D.l;
display palmer.l ;