# Adjiman 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 $x \in [-1, 2]$ and $y \in [-1, 1]$.

# Global Minima

On the on $x \in [-1, 2]$ and $x \in [-1, 1]$ cube, the global minimum $f(\textbf{x}^{\ast})=-2.02181$ is located at $\mathbf{x^\ast}=(0, 0)$.

# Implementation

An implementation of the **Adjiman 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
- C. S. Adjiman, S. Sallwig, C. A. Flouda, A. Neumaier, “A Global Optimization Method, aBB for General Twice-Differentiable NLPs-1, Theoretical Advances,” Computers Chemical Engineering, vol. 22, no. 9, pp. 1137-1158, 1998.
- Qing, A., “Differential Evolution: Fundamentals and Applications in Electrical Engineering”, Wiley, 2009. https://books.google.com/books?id=Pp-SHz6dIJ0C