Mathematical Definition
Input Domain
Matyas Function is usually evaluated on the square xi∈ [-10, 10], for all i = 1, 2.
Global Minima
The function has one global minimum f(𝑥∗)=0 at 𝑥∗ =(0,0)
Characteristics
The function is continuous.
The function is convex.
The function is defined on 2-D space.
The function is unimodal.
The function is differentiable.
The function is non-separable.
The function has no local minima except the global one
Python Implementation
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# Author: Dhanishtha Sharma
import sympy
import math
from sympy import symbols
from sympy import *
from sympy.plotting import plot3d
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
%matplotlib notebook
plt.rcParams['figure.figsize'] = (6,4)
plt.rcParams['figure.dpi']=150
fig=plt.figure()
ax=fig.add_subplot(111,projection='3d')
x1,x2=symbols('x1 x2')
plot3d(0.26*((x1**2)+(x2**2))-(0.48*x1*x2)) ,(x1,-10,10,2),(x2,-10,10,2)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.