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Python Implementation of MATYAS FUNCTION

Updated: Aug 5, 2021







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.




#optimization #benchmarkfunction

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