gemseo / problems / analytical

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rosenbrock module

The Rosenbrock analytic problem.

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

Bases: MDODiscipline

A multi-fidelity Rosenbrock discipline.

Its expression is \(\mathrm{fidelity} * \mathrm{Rosenbrock}(x)\) where both \(\mathrm{fidelity}\) and \(x\) are provided as input data.

Initialize self. See help(type(self)) for accurate signature.


dimension (int) –

The dimension of the design space.

By default it is set to 2.

cache: AbstractCache | None

The cache containing one or several executions of the discipline according to the cache policy.

data_processor: DataProcessor

A tool to pre- and post-process discipline data.

exec_for_lin: bool

Whether the last execution was due to a linearization.

input_grammar: BaseGrammar

The input grammar.

jac: MutableMapping[str, MutableMapping[str, ndarray | csr_array | JacobianOperator]]

The Jacobians of the outputs wrt inputs.

The structure is {output: {input: matrix}}.

name: str

The name of the discipline.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: ReExecutionPolicy

The policy to re-execute the same discipline.

residual_variables: dict[str, str]

The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.

run_solves_residuals: bool

Whether the run method shall solve the residuals.

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

Bases: OptimizationProblem

The Rosenbrock optimization problem.

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

with the default DesignSpace \([-0.2,0.2]^{n_x}\).

  • n_x (int) –

    The dimension of the design space.

    By default it is set to 2.

  • l_b (float) –

    The lower bound (common value to all variables).

    By default it is set to -2.0.

  • u_b (float) –

    The upper bound (common value to all variables).

    By default it is set to 2.0.

  • 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).

    By default it is set to False.

  • initial_guess (ndarray | None) – The initial guess for optimal solution.


Return the theoretical optimal value.


The design variables and the objective at optimum.

Return type:

tuple[ndarray, float]

constraints: list[MDOFunction]

The constraints.

current_iter: int

The current iteration.

database: Database

The database to store the optimization problem data.

design_space: DesignSpace

The design space on which the optimization problem is solved.

eq_tolerance: float

The tolerance for the equality constraints.

fd_step: float

The finite differences step.

ineq_tolerance: float

The tolerance for the inequality constraints.

max_iter: int

The maximum iteration.

new_iter_observables: list[MDOFunction]

The observables to be called at each new iterate.

nonproc_constraints: list[MDOFunction]

The non-processed constraints.

nonproc_new_iter_observables: list[MDOFunction]

The non-processed observables to be called at each new iterate.

nonproc_objective: MDOFunction

The non-processed objective function.

nonproc_observables: list[MDOFunction]

The non-processed observables.

observables: list[MDOFunction]

The observables.

pb_type: ProblemType

The type of optimization problem.

preprocess_options: dict

The options to pre-process the functions.

solution: OptimizationResult | None

The solution of the optimization problem if solved; otherwise None.

stop_if_nan: bool

Whether the optimization stops when a function returns NaN.

use_standardized_objective: bool

Whether to use standardized objective for logging and post-processing.

The standardized objective corresponds to the original one expressed as a cost function to minimize. A DriverLibrary works with this standardized objective and the Database stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.

Examples using Rosenbrock



Convert a database to a dataset

Convert a database to a dataset