Griewank Function

The Griewank function is a function widely used to test the convergence of optimization functions. The Griewank function of order  is defined by

for  (Griewank 1981), plotted above for . It has a global minimum of 0 at the point .

The function  has 191 minima, with global minimum at  and local minima at  for  (OEIS A177889), 12.5601, 18.8401, 25.1202, .... Restricting the domain of the function to , the numbers of local minima for  for , 2, ... are therefore given by 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, ... (OEIS A178832).

REFERENCES:

Cho, H.; Olivera, F.; and Guikema, S. D. "A Derivation of the Number of Minima of the Griewank Function." Appl. Math. Comput. 204, 694-701, 2008.

Griewank, A. O. "Generalized Decent for Global Optimization." J. Opt. Th. Appl. 34, 11-39, 1981.

Locatelli, M. "A Note on the Griewank Test Function." J. Global Opt. 25, 169-174, 2003.

Sloane, N. J. A. Sequences A177889 and A178832 in "The On-Line Encyclopedia of Integer Sequences."