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.