# gemseo_umdo.formulations¶

Formulations for multidisciplinary design problems under uncertainty.

A `MDOFormulation`

defines an `OptimizationProblem`

from one or several `DesignSpace`

,
an objective and constraints.
The objective can be either minimized (default) or maximized.

In the context of deterministic MDO,
the `OptimizationProblem`

is handled by a driver (see `DriverLib`

),
typically an optimizer (see `OptimizationLibrary`

),
or a design of experiments (DOE, see `DOELibrary`

).

In the frame of robust MDO,
the `UMDOFormulation`

uses a `MDOFormulation`

with a `ParameterSpace`

defining the uncertain variables
and executes the corresponding `OptimizationProblem`

with a particular DOE.
Then,
it post-processed the associated `Database`

to estimate the statistics applied to the objective and constraints.

The most common `UMDOFormulation`

is `Sampling`

,
consisting in estimating the statistics with (quasi) Monte Carlo techniques.