# Wolfe Function

# Mathematical Definition

# Description and Features

- The function is continuous.
- The function is not convex.
- The function is defined on 3-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 $x_i \in [0, 2]$ for $i=1, …, 3$.

# Global Minima

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

# Implementation

An implementation of the **Wolfe 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
- H. P. Schwefel, “Numerical Optimization for Computer Models,” John Wiley Sons, 1981.