OP_005

Objective

Topology Rosenbrock function
Models Single objective optimization module OP1
Simplex Algorithm
Outputs Position of the minimum
Parameters Optimization parameters: 10
See also OP_001
How to use MANATEE to optimize an external function

The objective of this validation case is to validate the Simplex algorithm used in MANATEE with the Rosenbrock function with 10 parameters. The Rosenbrock function has only one minimum and is very flat in the region around its minimum. It’s a standard function for optimization benchmarks.

960. 2D Rosenbrock function with its minimum in (1,1)
2D Rosenbrock function with its minimum in (1,1)

Equations

The Rosenbrock objective function si defined by:

f = \sum_{i=1}^{n-1}{100.(x_{i+1}^{2}-x_{i}^{2})+(1-x_{i}^{2})}

The solution is given by:

x=[1, 1, 1, ..., 1]

Here, we have 10 optimization parameters, n=10.

Results

960. Optimization results of Rosenbrock function
Optimization results of Rosenbrock function

The optimization process finds a minimum in [1, 1, 1, 1, 1, 1, 1, 1, 1, 1] with an absolute error under 10^{-7}.

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