# Qing 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 non-separable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-500, 500]$ for $i=1, …, n$.

# Global Minima

The global minima $f(\textbf{x}^{\ast})=0$ are located at $\mathbf{x^\ast}=(\pm\sqrt{i}, …, \pm\sqrt{i})$.

# Implementation

An implementation of the **Qing 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
- A. Qing, “Dynamic Differential Evolution Strategy and Applications in Electromagnetic Inverse Scattering Problems,” IEEE Transactions on Geoscience and remote Sensing, vol. 44, no. 1, pp. 116-125, 2006.