# Exponential Function

# Mathematical Definition

# Plots

A contour of the function is presented below:

# Description and Features

- The function is continuous.
- The function is convex.
- The function is defined on n-dimensional space.
- The function is unimodal.
- 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 $x_i \in [-1, 1]$ for $i=1, …, n$.

# Global Minima

The function has one global minimum $f(\textbf{x}^{\ast})=$ at $\mathbf{x^\ast}=0$.

# Implementation

An implementation of the **Exponential 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. Rahnamyan, H. R. Tizhoosh, N. M. M. Salama, “Opposition-Based Differential Evolution (ODE) with Variable Jumping Rate,” IEEE Sympousim Foundations Computation Intelligence, Honolulu, HI, pp. 81-88, 2007.