# Plots

Two contours of the function are as presented below:

# Description and Features

• The function is continuous.
• The function is not convex
• The function is defined on 2-dimensional space.
• The function is unimodal.
• The function is differentiable.
• The function is not separable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-100, 100]$ for $i=1, 2$.

# Global Minima

The function has one global minimum $f(\textbf{x}^{\ast})=0.00156685$ at $\textbf{x}^{\ast} = (0, 1.253115)$.

# Implementation

An implementation of the Schaffer N. 3 Function with MATLAB is provided below.

The function can be represented in Latex as follows:

# References:

• S. K. Mishra, “Some New Test Functions For Global Optimization And Performance of Repulsive Particle Swarm Method,” [Available Online]: http://mpra.ub.uni-muenchen.de/2718/
• Momin Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation}, Vol. 4, No. 2, pp. 150–194 (2013), arXiv:1308.4008