# Alpine N. 2 Function

# Mathematical Definition

# Plots

A contour of the function is presented below:

# Description and Features

- The function is not convex.
- The function is defined on n-dimensional space.
- The function is non-separable.
- The function is differentiable.

# Input Domain

The function can be defined on any positive input domain but it is usually evaluated on $x_i \in [0, 10]$ for $i=1, …, n$.

# Global Minima

The function was devised By Clerc as a maximization problem and hence, the orginial paper gave $f(\textbf{x}^{\ast})=2.808^n$, located at $\mathbf{x^\ast}=(7.917, …, 7.917)$, as its global maximum. The function can be used for minization by negating its value.

# Implementation

An implementation of the **Alpine N. 2 Function** with `MATLAB`

is provided below.

The function can be represented in Latex as follows:

# See Also:

# 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. Clerc, “The Swarm and the Queen, Towards a Deterministic and Adaptive Particle Swarm Optimization, ” IEEE Congress on Evolutionary Computation, Washington DC, USA, pp. 1951-1957, 1999.