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Python implementation of McCormick Function

Updated: Aug 5, 2021






Mathematical Definition



Input Domain

The input range of the func is: x1∈ [-1.5, 4], x2∈ [-3, 4].


Global Minima

The func has one global min f(x*)=-1.9133, at x* = (0.54719,-1.54719)


Characteristics

The function is continuous.

The function is  convex.

The function is defined on 2-D space.

The function is multimodal.

The function is differentiable.


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((sin(x1+x2)+(x1-x2)**2-1.5*x1+2.5*x2+1),(x1,-1.5,4,2),(x2,-3,4,2)) 





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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