# Shubert 4 Function

# Mathematical Definition

# Plots

Two contours of the function are 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 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 $f(\textbf{x}^{\ast})\approx-25.740858$.

# Implementation

An implementation of the **Shubert 4 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
- E. P. Adorio, U. P. Dilman, “MVF - Multivariate Test Function Library in C for Unconstrained Global Optimization Methods,” [Available Online]: http://www.geocities.ws/eadorio/mvf.pdf