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# QUARTIC FUNCTION

Updated: Jul 18, 2021

**Mathematical Definition**

**Input Domain**

The function can be defined on any input domain but it is usually evaluated on xi ∈[−1.28,1.28] for i=1,…,n. Here, n = 2.

**Global Minima**

The function has one global minimum f(x*)=0+random noise at x*=(0,…,0).

**Description and Features**

The function is continuous, not convex, defined on n-dimensional space, multimodal, differentiable, separable.

**Python Implementation**

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**%**** ****Author****:**** Sakshi Chadda**
**import**** **numpy **as**** **np
**import**** **matplotlib.pyplot **as**** **plt
**from**** **numpy **import**** **random
fig = plt.figure()
ax = fig.gca(projection=**'3d'**)
x = np.arange(-1.28, 1.28,0.1)
y = np.arange(-1.28, 1.28, 0.1)
x, y = np.meshgrid(x, y)
z = random.randint(0,1)
sum =0
**for**** **i **in**** **range(3):
sum = sum + (i * (x**4 + y **4))
result = sum + z
surface = ax.plot_surface(x, y, result, cmap=**'jet'**)
plt.show()
plt.contour(x,y,result)
plt.show()
plt.scatter(x, y, result)
plt.show()

**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.