# Goldstein-Price Function

# Mathematical Definition

# Plots

The contour of the function is as 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 .
- The function is non-scalable.

# Input Domain

The function can be defined on any input domain but it is usually evaluated on $x \in [-2, 2]$ and $y \in [-2, 2]$ .

# Global Minima

The function has four global minima $f(\textbf{x}^{\ast})=3$ at $\textbf{x}^{\ast} = (0, -1)$.

# Implementation

An implementation of the **Goldstein-Price Function** with MATLAB is provided below.

The function can be represented in Latex as follows:

# References:

- http://www.sfu.ca/~ssurjano/goldpr.html
- https://en.wikipedia.org/wiki/Test_functions_for_optimization
- 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