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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()
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.