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 .