The Rosenbrock function, also known as Rosenbrock's banana function or Rosenbrock's valley, is the function defined by
 |
that is often used as a test problem for optimization algorithms due to the existence of a global minimum of 0 at the point 
which is difficult to find.
The parameters are most commonly taken as 
and 
(though 
is sometimes also used; Germundsson 2000), as illustrated
above in the 
plane.
The function with 
and 
is plotted above for 
and 
.
