# Egg Crate 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 2-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 $x_i \in [-5, 5]$ for $i=1, 2$.

# Global Minima

The global minimum $f(\textbf{x}^{\ast})=0$ is located at $\mathbf{x^\ast}=(0, 0)$.

# Implementation

An implementation of the **Egg Crate 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://al-roomi.org/benchmarks/unconstrained/2-dimensions/122-egg-crate-function
- Chawdhry, P. K., Roy, R., & Pant, R. K. (2012). Soft Computing in Engineering Design and Manufacturing. London: Springer Science & Business Media.
- Yang, X.S. (2008). Nature-Inspired Metaheuristic Algorithms, Luniver Press.