TOPICS
Search

Rosenbrock Function


The Rosenbrock function, also known as Rosenbrock's banana function or Rosenbrock's valley, is the function defined by

 f(x,y)=(a-x)^2+b(y-x^2)^2

that is often used as a test problem for optimization algorithms due to the existence of a global minimum of 0 at the point (a,a^2) which is difficult to find.

RosenbrockFunction3D

The parameters are most commonly taken as a=1 and b=100 (though b=105 is sometimes also used; Germundsson 2000), as illustrated above in the xy plane.

RosenbrockFunction

The function with a=1 and b=100 is plotted above for y=1 and x=1.


See also

Griewank Function

Explore with Wolfram|Alpha

References

Germundsson, R. "Mathematica Version 4." Mathematica J. 7, 497-524, 2000.Rosenbrock, H. H. "An Automatic Method for Finding the Greatest or Least Value of a Function." Computer J. 3, 175-184, 1960.

Referenced on Wolfram|Alpha

Rosenbrock Function

Cite this as:

Weisstein, Eric W. "Rosenbrock Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RosenbrockFunction.html

Subject classifications