gemseo / problems / analytical

# rosenbrock module¶

## The Rosenbrock analytic problem¶

class gemseo.problems.analytical.rosenbrock.RosenMF(dimension=2)[source]

RosenMF, a multi-fidelity Rosenbrock MDODiscipline, returns the value:

$\mathrm{fidelity} * \mathrm{Rosenbrock}(x)$

where both $$\mathrm{fidelity}$$ and $$x$$ are provided as input data.

The constructor defines the default inputs of the MDODiscipline, namely the default design parameter values and the fidelity.

Parameters

dimension (int) – problem dimension

class gemseo.problems.analytical.rosenbrock.Rosenbrock(n_x=2, l_b=- 2.0, u_b=2.0, scalar_var=False, initial_guess=None)[source]

Rosenbrock OptimizationProblem uses the Rosenbrock objective function

$f(x) = \sum_{i=2}^{n_x} 100(x_{i} - x_{i-1}^2)^2 + (1 - x_{i-1})^2$

with the default DesignSpace $$[-0.2,0.2]^{n_x}$$.

The constructor initializes the Rosenbrock OptimizationProblem by defining the DesignSpace and the objective function.

Parameters
• n_x (int) – problem dimension

• l_b (float) – lower bound (common value to all variables)

• u_b (float) – upper bound (common value to all variables)

• scalar_var (bool) – if True the design space will contain only scalar variables (as many as the problem dimension); if False the design space will contain a single multidimensional variable (whose size equals the problem dimension)

• initial_guess (numpy array) – initial guess for optimal solution

get_solution()[source]

Return the theoretical optimal value.

Returns

design variables values of optimized values, function value at optimum

Return type

numpy array