Analytical test case # 1

In this example, we consider a simple optimization problem to illustrate algorithms interfaces and MDOFunction.

Imports

from __future__ import annotations

from numpy import cos
from numpy import exp
from numpy import ones
from numpy import sin
from scipy import optimize

from gemseo import configure_logger
from gemseo.core.mdo_functions.mdo_function import MDOFunction

configure_logger()

<RootLogger root (INFO)>

Define the objective function

We define the objective function \(f(x)=\sin(x)-\exp(x)\) using an MDOFunction defined by the sum of MDOFunction s.

f_1 = MDOFunction(sin, name="f_1", jac=cos, expr="sin(x)")
f_2 = MDOFunction(exp, name="f_2", jac=exp, expr="exp(x)")
objective = f_1 - f_2

See also

The following operators are implemented: \(+\), \(-\) and \(*\). The minus operator is also defined.

objective

[f_1-f_2] = sin(x)-exp(x)

Minimize the objective function

We want to minimize this objective function over \([-2,2]\), starting from 1. We use scipy.optimize for illustration.

Note

MDOFunction objects are callable like a Python function.

x_0 = -ones(1)
opt = optimize.fmin_l_bfgs_b(
    objective.evaluate, x_0, fprime=objective.jac, bounds=[(-0.2, 2.0)]
)
opt

(array([-0.2]), -1.017400083873043, {'grad': array([0.16133582]), 'task': 'CONVERGENCE: NORM_OF_PROJECTED_GRADIENT_<=_PGTOL', 'funcalls': 1, 'nit': 0, 'warnflag': 0})