# Sum Squares Function

# Mathematical Definition

# Plots

A contour of the function is presented below:

# Description and Features

- The function is continuous.
- The function is convex.
- The function is defined on n-dimensional space.
- The function is unimodal.
- The function is differentiable.
- The function is separable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-10, 10]$ for $i=1, …, n$.

# Global Minima

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

# Implementation

An implementation of the **Sum Squares 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://www.sfu.ca/~ssurjano/sumsqu.html
- A.-R. Hedar, “Global Optimization Test Problems,” [Available Online]: http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm.