* 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-8-0

$Set N 35
Set m /m1*m%N%/;

Parameter X(m) / m1 -1.788963    , m2 -1.745329    , m3 -1.658063    ,
                 m4 -1.570796    , m5 -1.483530    , m6 -1.396263    ,
                 m7 -1.308997    , m8 -1.218612    , m9 -1.134464    ,
                 m10 -1.047198   , m11 -0.872665   , m12 -0.698132   ,
                 m13 -0.523599   , m14 -0.349066   , m15 -0.174533   ,
                 m16 0.0000000   , m17 1.788963    , m18 1.745329    ,
                 m19 1.658063    , m20 1.570796    , m21 1.483530    ,
                 m22 1.396263    , m23 1.308997    , m24 1.218612    ,
                 m25 1.134464    , m26 1.047198    , m27 0.872665    ,
                 m28 0.698132    , m29 0.523599    , m30 0.349066    ,
                 m31 0.174533    , m32 -1.8762289  , m33 -1.8325957  ,
                 m34 1.8762289   , m35 1.8325957   / ;

Parameter Y(m) /  m1 78.596218   ,  m2 65.77963    ,  m3 43.96947    ,
                  m4 27.038816   ,  m5 14.6126     ,  m6 6.2614      ,
                  m7 1.538330    ,  m8 0.000000    ,  m9 1.188045    ,
                 m10 4.6841      , m11 16.9321     , m12 33.6988     ,
                 m13 52.3664     , m14 70.1630     , m15 83.4221     ,
                 m16 88.3995     , m17 78.596218   , m18 65.77963    ,
                 m19 43.96947    , m20 27.038816   , m21 14.6126     ,
                 m22 6.2614      , m23 1.538330    , m24 0.000000    ,
                 m25 1.188045    , m26 4.6841      , m27 16.9321     ,
                 m28 33.6988     , m29 52.3664     , m30 70.1630     ,
                 m31 83.4221     , m32 108.18086   , m33 92.733676   ,
                 m34 108.18086   , m35 92.733676   / ;

Variable A0 , A2 , A4 , A6 , A8 , A10 , L , K , palmer ;

Equation Def_obj ;

Def_obj.. palmer=e=       sum{m, sqr(Y[m]-(A0 +A2*power(X[m], 2) +
                                               A4*power(X[m], 4) +
                                               A6*power(X[m], 6) +
                                               A8*power(X[m], 8) +
                                              A10*power(X[m],10) +
                                      L * exp(-1*K*( sqr(X[m]) )) ))} ;

 A0.l  = 1.0 ;
 A2.l  = 1.0 ;
 A4.l  = 1.0 ;
 A6.l  = 1.0 ;
 A8.l  = 1.0 ;
A10.l  = 1.0 ;
 L.l   = 1.0 ;
 K.l   = 4.0 ;

* AMPL solution (will open only one to recieve the same)
*  A0.fx  = 73.6696
*  A2.fx = -106.078
*  A4.fx = 43.5928
*  A6.fx = -4.59074
*  A8.fx = 0.647315
* A10.fx = -0.0581003
*   L.fx = 14.7279
*   K.fx = 4.24197


Model palmer1e /all/ ;

Solve palmer1e using nlp minimazing palmer ;

display A0.l,A2.l,A4.l,A6.l,A8.l,A10.l,L.l,K.l;