# Schwefel 2.21 Function

# Mathematical Definition

# Plots

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 non-differentiable.
- The function is separable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-100, 100]$ 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 **Schwefel 2.21 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
- H. P. Schwefel, “Numerical Optimization for Computer Models,” John Wiley Sons, 1981.