* AMPL Model by Hande Y. Benson
*
* Copyright (C) 2001 Princeton University
* All Rights Reserved
*
* Permission to use, copy, modify, and distribute this software nd
* 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 N 23
Set m /m1*m%N%/;

Parameter X(m) /   m1    -1.745329  ,  m2    -1.570796  ,  m3    -1.396263  ,
                   m4    -1.221730  ,  m5    -1.047198  ,  m6    -0.937187  ,
                   m7    -0.872665  ,  m8    -0.698132  ,  m9    -0.523599  ,
                  m10    -0.349066  , m11    -0.174533  , m12    0.0        ,
                  m13     0.174533  , m14     0.349066  , m15    0.523599   ,
                  m16     0.698132  , m17     0.872665  , m18    0.937187   ,
                  m19     1.047198  , m20     1.221730  , m21    1.396263   ,
                  m22     1.570796  , m23     1.745329 /;

Parameter Y(m) /   m1    72.676767  ,  m2   40.149455   ,  m3   18.8548     ,
                   m4    6.4762     ,  m5    0.8596     ,  m6    0.00000    ,
                   m7    0.2730     ,  m8    3.2043     ,  m9    8.1080     ,
                  m10   13.4291     , m11   17.714      , m12   19.4529     ,
                  m13   17.7149     , m14   13.4291     , m15    8.1080     ,
                  m16    3.2053     , m17    0.2730     , m18    0.00000    ,
                  m19    0.8596     , m20    6.4762     , m21   18.8548     ,
                  m22   40.149455   , m23   72.676767 / ;

Positive Variable B , C , D  ;
Variable A , palmer ;

Equation Def_obj ;

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

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

* AMPL solution
*A.fx = 15.044
*B.fx = 2.4635e+17
*C.fx = 1.08231e+16
*D.fx = 3.60926e-18


Model palmer2 /all/ ;

Solve palmer2 using nlp minimazing palmer ;

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