ConstrainedOptProblem

Overview¶

ConstrainedOptProblem represents a nonlinear constrained optimization problem by combining objective terms, equality constraints, and inequality constraints into one object.

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¶

Objective terms are stored as a NonlinearFactorGraph.
Equality constraints enforce h(x)=0 through NonlinearEqualityConstraints.
Inequality constraints enforce g(x)<=0 through NonlinearInequalityConstraints.
The evaluate method reports cost and both constraint-violation norms.
auxiliaryProblem can transform inequality constraints into an equivalent equality-constrained form with auxiliary variables.

Mathematical Formulation¶

A constrained problem is modeled as:

\min_{x}\; \frac{1}{2}\|f(x)\|^2 \quad \text{s.t.}\; h(x)=0,\; g(x)\le 0.

(1)

ConstrainedOptProblem stores exactly these three components: costs $f$ , equality constraints $h$ , and inequality constraints $g$ . Its evaluate method reports objective cost plus equality/inequality violation magnitudes.

Key User API¶

ConstrainedOptProblem(costs, eqConstraints, ineqConstraints)
EqConstrainedOptProblem(costs, eqConstraints)
costs(), eConstraints(), iConstraints()
evaluate(values)
dim()
auxiliaryProblem(values, generator) for inequality-to-equality reformulation

Concise C++ Example¶

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

using namespace gtsam;

Symbol x1('x', 1), x2('x', 2);
Double_ X1(x1), X2(x2);

NonlinearFactorGraph costs;
auto noise = noiseModel::Isotropic::Sigma(1, 1.0);
costs.addPrior(x1, 1.0, noise);
costs.addPrior(x2, 1.0, noise);

NonlinearEqualityConstraints eq;
eq.emplace_shared<ExpressionEqualityConstraint<double>>(
    X1 * X1 + X2 * X2, 1.0, Vector1(1.0));

NonlinearInequalityConstraints ineq;
ineq.emplace_shared<ScalarExpressionInequalityConstraint>(
    4 * X1 * X1 + 0.25 * X2 * X2 - Double_(1.0), 1.0);

ConstrainedOptProblem problem(costs, eq, ineq);