* 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 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   / ;

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*power(X[m],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 =   1.0 ;
  K.l =   1.0 ;

* AMPL solution  (will be enouph to open only one)
*A0.fx = -8.31641
*A2.fx = 8.02445
*A4.fx = -12.0751
*A6.fx = 12.572
*A8.fx = -3.07426
*A10.fx = 0.297052
*L.fx = 27.6755
*K.fx = 2.27063







Model palmer2e /all/ ;

Solve palmer2e using nlp minimazing palmer ;

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