Mathematical optimization | Functions and mappings | Polynomials

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 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. (Wikipedia).

Rosenbrock function
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Test functions for optimization | Convex function | Sturm's theorem | Fundamental theorem of algebra | Mathematical optimization | Gradient descent | Parabola | Algorithm | Adaptive coordinate descent | Nelder–Mead method