Test functions for optimization: Difference between revisions

Revision as of 18:54, 22 January 2013

Revision as of 18:56, 22 January 2013

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! Sphere function

| <math>f(\boldsymbol{x}) = \sum_{i=1}^{n} x_{i}^{2}.\quad</math> || <math>f(x_{1}, \dots, x_{n}) = f(0, \dots, 0) = 0</math>, for <math>-\infty \le x_{i} \le \infty</math>, <math>1 \le i \le n</math> || [[File:Sphere function in 3D.pdf|300px|thumb||Sphere function for n=3.]]

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! [[Rosenbrock function]]

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n=2 & \rightarrow \quad f(1,1) = 0, \\

n=3 & \rightarrow \quad f(1,1,1) = 0, \\

n>3 & \rightarrow \quad f\left(-1,\underbrace{1,\dots,1}_{(n-1) \text{ times}}\right) = 0. \\

\end{cases}

</math> for <math>-\infty \le x_{i} \le \infty</math>, <math>1 \le i \le n</math> || [[File:Rosenbrock's function in 3D.pdf|300px|thumb||Rosenbrock's function for n=3.]]

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</math>

: .

: for <math>-\infty \le x_{i} \le \infty</math>, <math>1 \le i \le n</math>.

* Beale's function