* 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:
*   A.R. Conn, N. Gould and Ph.L. Toint,
*   "The LANCELOT User's Manual",
*   Dept of Maths, FUNDP, 1991.

*   SIF input: Ph. Toint, Jan 1991.

*   classification OLR2-AN-2-1

$Set N  5
Set I  / i1*i%N% / ;

Parameter c ; c = 0.85;
Parameter x[i] / i1       0.1   , i2       0.3   , i3       0.5   ,
                 i4       0.7   , i5       0.9   /;

Parameter y[i] / i1       0.25  , i2       0.3   , i3       0.625 ,
                 i4       0.701 , i5       1.0   /;

Positive Variable a ;

Variable b , f ;

Equation cons1 ,  Def_obj ;

cons1.. a*c =l= 0.0;

Def_obj.. f =e= sum{i,(
        ((abs{(a*x[i]*y[i])-15} + {(a*x[i]*y[i])-15})/2)/{(a*x[i]*y[i])-15}*
               0.5*( 1.5*abs(a*x[i]*y[i]) - 0.5*2.25) +
        ((abs{(a*x[i]*y[i])-15} - {(a*x[i]*y[i])-15})/2)/{(a*x[i]*y[i])-15}*
               0.5*( sqr(abs(a*x[i]*y[i]))          )
                   )  };

Model hubfit /all/ ;

Solve hubfit  using dnlp minimazing f ;

Display x ;
Display f.l ;