# Plots

A contour of the function is 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 non-separable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-20, 20]$ for $i=1, …, n$.

# Global Minima

The global minima $f(\textbf{x}^{\ast})=-24771.09375$ are located at $\mathbf{x^\ast}=(0, \pm 15)$.

# Implementation

An implementation of the Deckkers-Aarts 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
• M. M. Ali, C. Khompatraporn, Z. B. Zabinsky, “A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems,” Journal of Global Optimization, vol. 31, pp. 635-672, 2005.