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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 artificial landscapes presented herein for single-objective optimization problems are taken from Bäck, [1] Haupt et al. [2] and from Rody Oldenhuis software. [3] Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and ...
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]
Figure 1: MCS algorithm (without local search) applied to the two-dimensional Rosenbrock function. The global minimum = is located at (,) = (,). MCS identifies a position with within 21 function evaluations. After additional 21 evaluations the optimal value is not improved and the algorithm terminates.
The most common quasi-Newton algorithms are currently the SR1 formula (for "symmetric rank-one"), the BHHH method, the widespread BFGS method (suggested independently by Broyden, Fletcher, Goldfarb, and Shanno, in 1970), and its low-memory extension L-BFGS. The Broyden's class is a linear combination of the DFP and BFGS methods.
English: This function is very popular in Optimization. It is used as a test function in order to evaluate the performance of optimization algorithms. It is used as a test function in order to evaluate the performance of optimization algorithms.
In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed in 1974 by Rastrigin [1] as a 2-dimensional function and has been generalized by Rudolph. [2]
Pages in category "Test functions for optimization" ... Rosenbrock function; S. Shekel function This page was last edited on 29 December 2023, at 15:34 ...