Rosenbrock Function

The Rosenbrock function is a non-convex function used as a performance test problem for optimization

In mathematical optimization, the Rosenbrock function is a non-convex function used as a performance test problem for optimization algorithms introduced by Howard H. Rosenbrock in 1960[1]. It is also known as Rosenbrock's valley or Rosenbrock's banana function.

The global minimum is inside a long, narrow, parabolic shaped flat valley. To find the valley is trivial. To converge to the global minimum, however, is difficult.

It is defined by

f(x, y) = (1-x)^2 + 100(y-x^2)^2

It has a global minimum at (x, y)=(1, 1) where f(x, y)=0. A different coefficient of the second term is sometimes given, but this does not affect the position of the global minimum.