NonlinearConstraint - GTSAM Docs

Overview¶

NonlinearConstraint is the abstract base for constrained factors in the constrained module, built on top of NoiseModelFactor with constrained noise models.

Authors: Frank Dellaert, et al. (see THANKS for the full author list)

See LICENSE for the license information

try:
    import google.colab
    %pip install --quiet gtsam-develop
except ImportError:
    pass

Key Concepts¶

violation computes the constraint violation magnitude from factor error.
feasible checks whether a Values assignment satisfies a tolerance.
penaltyFactor builds an L2 penalty factor for constrained optimization methods.
Derived classes specialize behavior for equality and inequality constraints.

Mathematical Formulation¶

A nonlinear constraint is treated as a residual map $c(x)$ (with constrained noise scaling). A common penalty used by constrained solvers is:

\phi(x;\mu)=\frac{\mu}{2}\|c(x)\|^2.

(1)

This class provides the shared interface for evaluating constraint violation and creating a penalty factor used in outer-loop constrained optimization.

Key User API¶

violation(values)
feasible(values, tolerance)
penaltyFactor(mu)
sigmas()
unwhitenedHessian(values) (advanced)

Concise C++ Example¶

#include <gtsam/constrained/NonlinearEqualityConstraint.h>
#include <gtsam/nonlinear/expressions.h>

using namespace gtsam;

Symbol x('x', 0);
Double_ X(x);
ExpressionEqualityConstraint<double> c(X * X, 1.0, Vector1(0.1));

Values values;
values.insert(x, 0.8);

bool ok = c.feasible(values, 1e-3);
double v = c.violation(values);
auto penalty = c.penaltyFactor(10.0);