function f = local ( x )

%% LOCAL computes the local function.
%
%  Discussion:
%
%    This function has a local minimum:
%
%      X* = (  0.28581..., 0.27936...), F(X*) = 5.9225...
%
%    and a global minimum:
%
%      X* = (  -21.026653..., -36.760090...), F(X*) = 0.
%
%    Suggested starting point:
%
%      X = ( 1, 1 ), F(X) = 3.33 * 10^6.
%
%  Modified:
%
%    12 February 2008
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    David Himmelblau,
%    Applied Nonlinear Programming,
%    McGraw Hill, 1972,
%    ISBN13: 978-0070289215,
%    LC: T57.8.H55.
%
%  Parameters:
%
%    Input, real X(2), the argument of the function.
%
%    Output, real F, the value of the function at X.
%
  if ( length ( x ) ~= 2 )
    error ( 'Error: function expects a two dimensional input\n' );
  end

  f = ( x(1)^2 + 12 * x(2) - 1 )^2 ...
    + ( 49 * x(1)^2 + 49 * x(2)^2 + 84 * x(1) + 2324 * x(2) - 681 )^2;