rosenbrock
The Rosenbrock function is unimodal, and the global minimum lies in a narrow, parabolic valley [1].
of = rosenbrock(x)
Input variables
| Name | Description | Type |
|---|---|---|
x | Current design variables of the i agent. | List |
Output variables
| Name | Description | Type |
|---|---|---|
of | Objective function value of the i agent. | Float |
Problem
| \[f(\mathbf{x}) = \sum_{i=1}^{d-1}\left [ 100 \left ( x_{i+1} - x_{i}^{2} \right )_{}^{2} + \left ( x_{i} + 1 \right )_{}^{2} \right ] \] | (1) |
| \[ x_{i} \in [-5, 10], x_{i} \in [-5, 10], i=1, ... , d; \;...\; f(\mathbf{x}^*) = 0, \; \mathbf{x}^* = (1,...,1) \] | (2) |
Example 1
Considering the design variable \(\mathbf{x} = [1,1]\), what value does the objective function expect?
# Data
x = [1, 1]
# Call function
of = rosenbrock(x)
# Output details
print("of_best rosenbrock: of = {:.4f}".format(of))
of_best rosenbrock: of = 0.0000