# Rosenbrock¶

The definition ca be found in [32]. It is a non-convex function, introduced by Howard H. Rosenbrock in 1960 and also known as Rosenbrock’s valley or Rosenbrock’s banana function.

Definition

\begin{align} \begin{split} f(x) &=& \sum_{i=1}^{n-1} \bigg[100 (x_{i+1}-x_i^2)^2+(x_i - 1)^2 \bigg] \\ &&-2.048 \leq x_i \leq 2.048 \quad i=1,\ldots,n \end{split} \end{align}

Optimum

$f(x^*) = 0 \; \text{at} \; x^* = (1,\ldots,1)$

Contour

[1]:

import numpy as np
from pymoo.factory import get_problem, get_visualization

problem = get_problem("rosenbrock", n_var=2)
get_visualization("fitness-landscape", problem, angle=(45, 45), _type="surface").show()

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