Updated: Aug 5, 2021
The function can be defined on any input domain but it is usually evaluated on xi ∈ [−5, 10], xi ∈ [−5, 10] for i=1,…, n.
The function has one global minimum f(x∗)=0 at x∗=(1,…,1).
Description and Features
The function is continuous.
The function is convex.
The function is defined on n-dimensional space.
The function is multimodal.
The function is differentiable.
The function is non-separable.
% Please forward any comments or bug reports in chat Copyright 2021. INDUSMIC PRIVATE LIMITED.THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY FOR THE USE OF THIS PROGRAM. If software is modified to produce derivative works, such modified software should be clearly marked. Additionally, user can redistribute it and/or modify it under the terms of the GNU General Public License. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY. See the GNU General Public License for more details. % for any support connect with us on firstname.lastname@example.org % Author: Ayushi Manish Shukla from matplotlib import pyplot as plt from mpl_toolkits import mplot3d import numpy as np import matplotlib.pyplot as plt from matplotlib import cm def f(x1, x2): return 100*(x2-x1**2)**2+(x1-1)**2 x1 = np.linspace(-5, 10) x2 = np.linspace(-5, 10) X1, X2 = np.meshgrid(x1, x2) F = f(x1, x2) plt.contour(X1, X2, f(X1, X2)) def plotter(E, A): fig = plt.figure(figsize = [12, 8]) ax = plt.axes(projection='3d') ax.plot_surface(X1, X2, f(X1, X2), cmap='jet', alpha=0.8) ax.plot_wireframe(X1, X2, f(X1, X2), rcount=15, ccount=15) ax.view_init(elev=E, azim=A) ax.set_xlabel('X') ax.set_ylabel('Y') ax.set_zlabel('f(X, Y)') ax.contourf(x1, x2, f(X1, X2)) print("solution 2") plotter(45, 45) from ipywidgets import interactive iplot = interactive(plotter, E = (-90, 90, 5), A = (-90, 90, 5)) iplot
 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.