NonlinearInequalityConstraint

Overview¶

NonlinearInequalityConstraint defines constraints of the form g(x)<=0 and supports direct violation computation plus conversion into penalty terms.

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¶

ScalarExpressionInequalityConstraint is a scalar expression-based implementation.
penaltyFactor and penaltyFactorCustom map inequality violations into optimization costs.
createEqualityConstraint provides the corresponding boundary equality g(x)=0 when needed.
NonlinearInequalityConstraints aggregates multiple inequality constraints and builds combined penalty graphs.

Mathematical Formulation¶

Inequality constraints enforce:

g(x)\le 0.

(1)

The default violation mapping uses a ramp on each component:

\text{ramp}(u)=\max(u,0),\quad \phi(x;\mu)=\frac{\mu}{2}\|\text{ramp}(g(x))\|^2.

(2)

This keeps inactive constraints from contributing cost while penalizing violated constraints.

Key User API¶

ScalarExpressionInequalityConstraint::LeqZero(expression, sigma)
ScalarExpressionInequalityConstraint::GeqZero(expression, sigma)
feasible(values, tolerance)
active(values)
penaltyFactor(mu) and penaltyFactorCustom(func, mu)
createEqualityConstraint()
NonlinearInequalityConstraints::penaltyGraph(mu)

Concise C++ Example¶

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

using namespace gtsam;

Symbol x1('x', 1), x2('x', 2);
Double_ X1(x1), X2(x2);
Double_ g = X1 + X1 * X1 * X1 + X2 + X2 * X2;

auto c = ScalarExpressionInequalityConstraint::LeqZero(g, 0.1);

Values values;
values.insert(x1, 1.0);
values.insert(x2, 1.0);

bool ok = c->feasible(values);
bool isActive = c->active(values);
auto p = c->penaltyFactor(9.0);