optimization/test_functions/extended_powell1.m

   1 function f = extended_powell1(x)
   2   %
   3   % The extended Powell function. See Dennis & Schnabel, Appendix B,
   4   % problem #2.
   5   %
   6   % This function has a minimum at x=(0,0,...,0) with f(x) == 0. The
   7   % suggested starting point is x0=(3, -1, 0, 1,..., 3, -1, 0, 1).
   8   % Since the number of arguments is variable, we take a vector
   9   % instead of its individual components.
  10   %
  11   n = length(x);
  12
  13   if (odd(n))
  14     % 'm' below must be an integer.
  15     f = NA;
  16     return;
  17   end
  18
  19   m = n / 4;
  20   f = 0;
  21
  22   % The extended Powell is simply a sum of Powell
  23   % applications.
  24   for k = [ 1 : m ]
  25     y1 = x(4*k - 3);
  26     y2 = x(4*k - 2);
  27     y3 = x(4*k - 1);
  28     y4 = x(4*k);
  29
  30     f_k = powell(y1,y2,y3,y4);
  31     f = f + f_k;
  32   end
  33 end