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==Test functions for single-objective optimization problems==
{| class="wikitable" style="text-align:center"
|+Test functions for single-objective optimization problems
|-
! Name !! Formula !! Minimum !! Search ___domain !! Plot
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|| <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> || <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]] |-
|| <math>f(\boldsymbol{x}) = \sum_{i=1}^{n-1} \left[ 100 \left(x_{i+1} - x_{i}^{2}\right)^{2} + \left(x_{i} - 1\right)^{2}\right].\quad</math>
|| <math>\text{Minimum} = \begin{cases}
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>
</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]]▼
|| <math>-\infty \le x_{i} \le \infty</math>, <math>1 \le i \le n</math>
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</math>
: for <math>-\infty \le x_{i} \le \infty</math>, <math>1 \le i \le n</math>.
* Beale's function
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