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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 ...
The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and Binh. [6] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which implements the NSGA-II procedure with ES.
The idea of Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's method) in Matlab. Rosenbrock search is a form of derivative-free search but may perform better on functions with sharp ridges. [6] The method often identifies such a ridge which, in many applications, leads to a solution. [7]
The short form of the Rosenbrock system matrix has been widely used in H-infinity methods in control theory, where it is also referred to as packed form; see command pck in MATLAB. [3] An interpretation of the Rosenbrock System Matrix as a Linear Fractional Transformation can be found in. [ 4 ]
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Specifically, function classes that ensure the existence of a sequence {^} that satisfies are known as learnable classes. [ 1 ] It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies ( 1 ). [ 2 ]
I recommend that this Wiki page lists only test functions if they are cited with the seminal source, which should be a permanently accessible reference, e.g. journal paper or Zenodo. A good example is H.H. Rosenbrock "An automatic method for finding the greatest or least value of a function" The Computer J. 1960. This will enable double-checking.