# Bird Function

# Mathematical Definition

# Plots

Two contours of the function are presented below:

# Description and Features

- The function is not convex.
- The function is defined on 2-dimensional space.
- The function is non-separable.
- The function is differentiable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-2\pi, 2\pi]$ for $i=1, 2$.

# Global Minima

The function has two global minima at $f(\textbf{x}^{\ast}) = -106.764537$ located at $\mathbf{x^\ast}=(4.70104, 3.15294)$ and $\mathbf{x^\ast}=(-1.58214, -3.13024)$.

# Implementation

An implementation of the **Bird 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
- S. K. Mishra, “Global Optimization By Differential Evolution and Particle Swarm Methods: Evaluation On Some Benchmark Functions,” Munich Research Papers in Economics, Available Online: http://mpra.ub.uni-muenchen.de/1005/.