* 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 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    -0.766531 ,  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    0.766531  , i18    0.872665  ,
                  i19    1.047198  , i20    1.221730  , i21    1.396263  ,
                  i22    1.570796  , i23    1.658063  / ;

Parameter Y[i]  / i1  64.87939     ,  i2  50.46046    ,  i3  28.2034     ,
                  i4  13.4575      ,  i5   4.6547     ,  i6   0.59447    ,
                  i7   0.0000      ,  i8   0.2177     ,  i9   2.3029     ,
                 i10   5.5191      , i11   8.5519     , i12   9.8919     ,
                 i13   8.5519      , i14   5.5191     , i15   2.3029     ,
                 i16   0.2177      , i17   0.0000     , i18   0.59447    ,
                 i19   4.6547      , i20  13.4575     , i21  28.2034     ,
                 i22  50.46046     , i23  64.87939    / ;

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

Def_obj.. palmer =e= sum{i, sqr(Y[i] -(A0 + A2*power(X[i],2)  +
                                            A4*power(X[i],4)  +
                                            A6*power(X[i],6)  +
                                            A8*power(X[i],8)  +
                                           A10*power(X[i],10) +
                                             exp(L-1*K*power(X[i],2)) ) )};
 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 = 0.0 ;
  K.l = 1.0 ;

Model palmer3e  /all/;

solve palmer3e  using nlp minimazing  palmer;

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