Rosenbrock function

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The Rosenbrock function is a mathematical function used as a test problem for optimisation algorithms. It is also known as Rosenbrock's Valley or Rosenbrock's Banana Function. It is defined by:

f(x,y) = (1 − x)2 + 100(yx2)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.