Rosenbrock function
Function used as a performance test problem for optimization algorithms / From Wikipedia, the free encyclopedia
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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.[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.
The function is defined by
It has a global minimum at , where . Usually, these parameters are set such that and . Only in the trivial case where the function is symmetric and the minimum is at the origin.