# Plots

Contour of the function is presented below:

# Description and Features

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

# Input Domain

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

# Global Minima

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

# Implementation

An implementation of the Salomon Function with MATLAB is provided below.

The function can be represented in Latex as follows:

# References:

• 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
• http://profesores.elo.utfsm.cl/~tarredondo/info/soft-comp/functions/node12.html
• R. Salomon, “Re-evaluating Genetic Algorithm Performance Under Corodinate Rotation of Benchmark Functions: A Survey of Some Theoretical and Practical Aspects of Genetic Algorithms,” BioSystems, vol. 39, no. 3, pp. 263-278, 1996.