* 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:
*   Ph.L. Toint,
*   "Some numerical results using a sparse matrix updating formula in
*   unconstrained optimization",
*   Mathematics of Computation, vol. 32(114), pp. 839-852, 1978.

*   See also Buckley#46 (n = 25) (p. 45).
*   SIF input: Ph. Toint, Dec 1989.

*   classification SUR2-AN-V-0

$Set N 50
Set i /i1*i%N%/;
Set left(i) /i2*i%N%/;

parameter alph(i) /i1 1.25, i2 1.40, i3 2.40, i4 1.40, i5 1.75,
                   i6 1.20, i7 2.25, i8 1.20, i9 1.00,i10 1.10,
                  i11 1.50,i12 1.60,i13 1.25,i14 1.25,i15 1.20,
                  i16 1.20,i17 1.40,i18 0.50,i19 0.50,i20 1.25,
                  i21 1.80,i22 0.75,i23 1.25,i24 1.40,i25 1.60,
                  i26 2.00,i27 1.00,i28 1.60,i29 1.25,i30 2.75,
                  i31 1.25,i32 1.25,i33 1.25,i34 3.00,i35 1.50,
                  i36 2.00,i37 1.25,i38 1.40,i39 1.80,i40 1.50,
                  i41 2.20,i42 1.40,i43 1.50,i44 1.25,i45 2.00,
                  i46 1.50,i47 1.25,i48 1.40,i49 0.60,i50 1.50 / ;

Variable   x[i] , f ;

Equation  Def_obj ;

Def_obj..  f=e=sum{i$left(i),
                    (sqr(x[i-1]-sqr(x[i]))*16*sqr(alph[i])+sqr(x[i]-1.0))  };

x.l[i]  =   -1.0    ;

Model chnrosnb /all/;

Solve chnrosnb using nlp minimize f;

display x.l;
display f.l;