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optimization > Rosenbrock function

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Rosenbrock function

In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. 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.
The function is defined by
${\\displaystyle f(x,y)=(a-x)^{2}+b(y-x^{2})^{2}}$
It has a global minimum at ${\\displaystyle (x,y)=(a,a^{2})}$ , where ${\\displaystyle f(x,y)=0}$ . Usually, these parameters are set such that ${\\displaystyle a=1}$ and ${\\displaystyle b=100}$ . Only in the trivial case where ${\\displaystyle a=0}$ the function is symmetric and the minimum is at the origin.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Rosenbrock_function)

fonction de Rosenbrock

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