Source code for gemseo.algos.first_order_stop_criteria

# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - API and implementation and/or documentation
#       :author: Simone Coniglio
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""Implementation of the Karush-Kuhn-Tucker residual norm stopping criterion."""

from __future__ import annotations

from typing import TYPE_CHECKING

from numpy.linalg import norm

from gemseo.algos.lagrange_multipliers import LagrangeMultipliers
from gemseo.algos.stop_criteria import TerminationCriterion

if TYPE_CHECKING:
from numpy import ndarray

from gemseo.algos.opt_problem import OptimizationProblem

[docs]
class KKTReached(TerminationCriterion):
"""A termination criterion based on the Karush-Kuhn-Tucker (KKT) residual norm."""

[docs]
def is_kkt_residual_norm_reached(
opt_problem: OptimizationProblem,
x_vect: ndarray,
kkt_abs_tol: float | None = 0.0,
kkt_rel_tol: float | None = 0.0,
ineq_tolerance: float = 1e-4,
reference_residual: float = 1.0,
) -> bool:
"""Test if the KKT conditions are satisfied.

Args:
opt_problem: The optimization problem containing an optimization history.
x_vect: The design point vector where the KKT conditions are tested.
kkt_abs_tol: The absolute tolerance on the KKT condition residual.
If None, the absolute criterion is not activated.
kkt_rel_tol: The relative tolerance on the KKT condition residual.
If None, the relative criterion is not activated.
ineq_tolerance: The tolerance to consider a constraint as active.
reference_residual: The reference KKT condition residual.

Returns:
Whether the absolute or the relative KKT residual norm criterion is reached.
"""
if kkt_abs_tol is None:
kkt_abs_tol = 0.0
if kkt_rel_tol is None:
kkt_rel_tol = 0.0
return kkt_residual_computation(opt_problem, x_vect, ineq_tolerance) <= max(
kkt_abs_tol, kkt_rel_tol * reference_residual
)

[docs]
def kkt_residual_computation(
opt_problem: OptimizationProblem,
x_vect: ndarray,
ineq_tolerance: float = 1e-4,
) -> float:
"""Compute the KKT residual norm.

This implementation is inspired from Svanberg Matlab implementation of
MMA algorithm see :cite:svanberg1998method

Args:
opt_problem: The optimization problem containing an optimization history.
x_vect: The design point vector where the KKT conditions are tested.
ineq_tolerance: The tolerance to consider a constraint as active.

Returns:
The KKT residual norm.
"""
res = opt_problem.database.get_function_value(opt_problem.KKT_RESIDUAL_NORM, x_vect)
if res is not None:
return res
lagrange = LagrangeMultipliers(opt_problem)
if opt_problem.has_constraints():
lagrange.compute(x_vect, ineq_tolerance=ineq_tolerance)
res = lagrange.kkt_residual + lagrange.constraint_violation
opt_problem.database.store(x_vect, {opt_problem.KKT_RESIDUAL_NORM: res})
return res

res = norm(lagrange.get_objective_jacobian(x_vect))
opt_problem.database.store(x_vect, {opt_problem.KKT_RESIDUAL_NORM: res})
return res