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# Brown Function

Updated: Jul 18, 2021  Mathematical Definition Input Domain

Brown Function is usually evaluated for the range: -1≤ xi≤ 4 for i=1,….,n. This function is smooth.

Global Minima

The function has one global minimum f (x*) = =0 at x*=(0,...,0)

Description and Features

Brown Function is a unimodal optimization problem. It is scalable and is defined on n- dimensional space.

Python Implementation

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import matplotlib.pyplot as plt
import matplotlib as mpl
from mpl_toolkits import mplot3d
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
from numpy import*
%matplotlib notebook
plt.rcParams['figure.figsize'] = (6,4)
plt.rcParams['figure.dpi']=150
fig=plt.figure()
axis = fig.gca(projection= '3d')

def f(x1,x2):
a= (x1*x1)**(x2*x2 + 1) + (x2*x2)**(x1*x1 +1)
return a
x1= linspace(4,-4)
x2= linspace(4,-4)
X1,X2= meshgrid(x1,x2)
ax.plot_surface(X1,X2,f(X1,X2), cmap='jet')
ax.set_xlabel('x')
ax.set_ylabel('y')
axis.view_init(10,10)
plt.show```

References:

 Jamil, Momin, and Xin-She Yang. "A literature survey of benchmark functions for global optimization problems." International Journal of Mathematical Modelling and Numerical Optimization 4.2 (2013): 150-194.