Schwefel 2.21

Mathematical Definition
Latex
f(x) = {\max_{i=1,...,n}|x_i|}
Description and Features

Dimensions: d

The function has one global minimum. It is continuous, convex and unimodal. The plot shows its two-dimensional form.

  • The function is continuous.
  • The function is convex.
  • The function is defined on n-dimensional space.
  • The function is unimodal.
  • The function is non-differentiable.
  • The function is separable.
Input Domain

The function can be defined on any input domain but it is usually evaluated on $x_i \in [-100, 100]$ for $i = 1, …, d$ .

Global Minima

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

Implementation
Python Code

def function(x):
    x = np.array(x)
    return np.max(np.abs(x))

            
Solutions
References:
  • http://benchmarkfcns.xyz/benchmarkfcns/schwefel221fcn.html
  • 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.