Mathematical Definition
Input Domain
The function is defined on input domain i.e. x ∈ [−1, 2] and y ∈ [−1, 1].
Global Minima
The global minimum f(z) = −2.02181 is located at z = (0, 0).
Characteristics
The function is not convex.
The function is differentiable.
The function is non-separable.
The function is defined on 2-dimensional space.
Python Implementation
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% Author: Yamini Jain
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import cm
def f(x,y):
return (np.cos(x)*np.sin(y) - (x/(y**2+1)))
X = np.linspace(-1,2)
Y = np.linspace(-1,1)
x,y = np.meshgrid(X,Y) #creating a rough mesh for generation of graph
F = f(x,y)
fig = plt.figure(figsize=(9,9))
ax = plt.axes(projection='3d')
ax.contour3D(x,y, F,450, cmap = cm.cubehelix_r)
ax.set_title('Adijman Function') #Giving a title to the image
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('F')
ax.set_xlim(2,-1)
ax.set_ylim(1,-1)
ax.set_zlim(-3,2)
ax.view_init(21,45) #This can be altered according to the need
plt.show()
References:
[1] 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.