274 lines
9.1 KiB
C++
274 lines
9.1 KiB
C++
/* ----------------------------------------------------------------------------
|
|
|
|
* GTSAM Copyright 2010, Georgia Tech Research Corporation,
|
|
* Atlanta, Georgia 30332-0415
|
|
* All Rights Reserved
|
|
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
|
|
|
|
* See LICENSE for the license information
|
|
|
|
* -------------------------------------------------------------------------- */
|
|
|
|
/**
|
|
* @file testQPSimple.cpp
|
|
* @brief Unit tests for testQPSimple
|
|
* @author Krunal Chande
|
|
* @author Duy-Nguyen Ta
|
|
* @author Luca Carlone
|
|
* @date Dec 15, 2014
|
|
*/
|
|
|
|
#include <gtsam/inference/Symbol.h>
|
|
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
|
|
#include <gtsam/nonlinear/LinearContainerFactor.h>
|
|
#include <gtsam_unstable/linear/QPSolver.h>
|
|
#include <gtsam_unstable/nonlinear/NonlinearConstraint.h>
|
|
#include <CppUnitLite/TestHarness.h>
|
|
#include <iostream>
|
|
|
|
namespace gtsam {
|
|
|
|
class LinearEqualityManifoldFactorGraph: public FactorGraph<NonlinearFactor> {
|
|
public:
|
|
/// default constructor
|
|
LinearEqualityManifoldFactorGraph() {
|
|
}
|
|
|
|
/// linearize to a LinearEqualityFactorGraph
|
|
LinearEqualityFactorGraph::shared_ptr linearize(
|
|
const Values& linearizationPoint) const {
|
|
LinearEqualityFactorGraph::shared_ptr linearGraph(
|
|
new LinearEqualityFactorGraph());
|
|
BOOST_FOREACH(const NonlinearFactor::shared_ptr& factor, *this){
|
|
JacobianFactor::shared_ptr jacobian = boost::dynamic_pointer_cast<JacobianFactor>(
|
|
factor->linearize(linearizationPoint));
|
|
NonlinearConstraint::shared_ptr constraint = boost::dynamic_pointer_cast<NonlinearConstraint>(factor);
|
|
linearGraph->add(LinearEquality(*jacobian, constraint->dualKey()));
|
|
}
|
|
return linearGraph;
|
|
}
|
|
|
|
/**
|
|
* Return true if the max absolute error all factors is less than a tolerance
|
|
*/
|
|
bool checkFeasibility(const Values& values, double tol) const {
|
|
BOOST_FOREACH(const NonlinearFactor::shared_ptr& factor, *this){
|
|
NoiseModelFactor::shared_ptr noiseModelFactor = boost::dynamic_pointer_cast<NoiseModelFactor>(
|
|
factor);
|
|
Vector error = noiseModelFactor->unwhitenedError(values);
|
|
if (error.lpNorm<Eigen::Infinity>() > tol) {
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
};
|
|
|
|
class NonlinearEqualityFactorGraph: public LinearEqualityManifoldFactorGraph {
|
|
public:
|
|
/// default constructor
|
|
NonlinearEqualityFactorGraph() {
|
|
}
|
|
|
|
GaussianFactorGraph::shared_ptr multipliedHessians(const Values& values, const VectorValues& duals) const {
|
|
GaussianFactorGraph::shared_ptr constrainedHessians(new GaussianFactorGraph());
|
|
BOOST_FOREACH(const NonlinearFactor::shared_ptr& factor, *this) {
|
|
NonlinearConstraint::shared_ptr constraint = boost::dynamic_pointer_cast<NonlinearConstraint>(factor);
|
|
constrainedHessians->push_back(constraint->multipliedHessian(values, duals));
|
|
}
|
|
return constrainedHessians;
|
|
}
|
|
};
|
|
|
|
|
|
struct NLP {
|
|
NonlinearFactorGraph cost;
|
|
NonlinearEqualityFactorGraph linearEqualities;
|
|
NonlinearEqualityFactorGraph nonlinearEqualities;
|
|
};
|
|
|
|
struct SQPSimpleState {
|
|
Values values;
|
|
VectorValues duals;
|
|
bool converged;
|
|
|
|
/// Default constructor
|
|
SQPSimpleState() : values(), duals(), converged(false) {}
|
|
|
|
/// Constructor with an initialValues
|
|
SQPSimpleState(const Values& initialValues) :
|
|
values(initialValues), duals(VectorValues()), converged(false) {
|
|
}
|
|
};
|
|
|
|
/**
|
|
* Simple SQP optimizer to solve nonlinear constrained problems.
|
|
* This simple version won't care about nonconvexity, which needs
|
|
* more advanced techniques to solve, e.g., merit function, line search, second-order correction etc.
|
|
*/
|
|
class SQPSimple {
|
|
NLP nlp_;
|
|
static const double errorTol = 1e-5;
|
|
public:
|
|
SQPSimple(const NLP& nlp) :
|
|
nlp_(nlp) {
|
|
}
|
|
|
|
/// Check if \nabla f(x) - \lambda * \nabla c(x) == 0
|
|
bool isDualFeasible(const VectorValues& delta) const {
|
|
return delta.vector().lpNorm<Eigen::Infinity>() < errorTol;
|
|
}
|
|
|
|
/// Check if c(x) == 0
|
|
bool isPrimalFeasible(const SQPSimpleState& state) const {
|
|
return nlp_.linearEqualities.checkFeasibility(state.values, errorTol)
|
|
&& nlp_.nonlinearEqualities.checkFeasibility(state.values, errorTol);
|
|
}
|
|
|
|
/// Check convergence
|
|
bool checkConvergence(const SQPSimpleState& state, const VectorValues& delta) const {
|
|
return isPrimalFeasible(state) & isDualFeasible(delta);
|
|
}
|
|
|
|
/**
|
|
* Single iteration of SQP
|
|
*/
|
|
SQPSimpleState iterate(const SQPSimpleState& state) const {
|
|
// construct the qp subproblem
|
|
QP qp;
|
|
qp.cost = *nlp_.cost.linearize(state.values);
|
|
GaussianFactorGraph::shared_ptr multipliedHessians = nlp_.nonlinearEqualities.multipliedHessians(state.values, state.duals);
|
|
qp.cost.push_back(*multipliedHessians);
|
|
|
|
qp.equalities.add(*nlp_.linearEqualities.linearize(state.values));
|
|
qp.equalities.add(*nlp_.nonlinearEqualities.linearize(state.values));
|
|
|
|
// solve the QP subproblem
|
|
VectorValues delta, duals;
|
|
QPSolver qpSolver(qp);
|
|
boost::tie(delta, duals) = qpSolver.optimize();
|
|
|
|
// update new state
|
|
SQPSimpleState newState;
|
|
newState.values = state.values.retract(delta);
|
|
newState.duals = duals;
|
|
newState.converged = checkConvergence(newState, delta);
|
|
|
|
return newState;
|
|
}
|
|
|
|
/**
|
|
* Main optimization function.
|
|
*/
|
|
std::pair<Values, VectorValues> optimize(const Values& initialValues) const {
|
|
SQPSimpleState state(initialValues);
|
|
while (!state.converged) {
|
|
state = iterate(state);
|
|
}
|
|
|
|
return std::make_pair(initialValues, VectorValues());
|
|
}
|
|
|
|
|
|
};
|
|
}
|
|
|
|
using namespace std;
|
|
using namespace gtsam::symbol_shorthand;
|
|
using namespace gtsam;
|
|
const double tol = 1e-10;
|
|
//******************************************************************************
|
|
TEST(testSQPSimple, Problem2) {
|
|
// Simple quadratic cost: x1^2 + x2^2
|
|
// Note the Hessian encodes:
|
|
// 0.5*x1'*G11*x1 + x1'*G12*x2 + 0.5*x2'*G22*x2 - x1'*g1 - x2'*g2 + 0.5*f
|
|
// Hence here we have G11 = 2, G12 = 0, G22 = 2, g1 = 0, g2 = 0, f = 0
|
|
HessianFactor hf(X(1), X(2), 2.0 * ones(1,1), zero(1), zero(1),
|
|
2*ones(1,1), zero(1) , 0);
|
|
|
|
LinearEqualityFactorGraph equalities;
|
|
equalities.push_back(LinearEquality(X(1), ones(1), X(2), ones(1), -1*ones(1), 0)); // x + y - 1 = 0
|
|
|
|
// Compare against QP
|
|
QP qp;
|
|
qp.cost.add(hf);
|
|
qp.equalities = equalities;
|
|
|
|
// instantiate QPsolver
|
|
QPSolver qpSolver(qp);
|
|
// create initial values for optimization
|
|
VectorValues initialVectorValues;
|
|
initialVectorValues.insert(X(1), zero(1));
|
|
initialVectorValues.insert(X(2), zero(1));
|
|
VectorValues expectedSolution = qpSolver.optimize(initialVectorValues).first;
|
|
cout<<"expectedSolution.at(X(1))[0]: "<<expectedSolution.at(X(1))[0]<<endl;
|
|
cout<<"expectedSolution.at(X(2))[0]: "<<expectedSolution.at(X(2))[0]<<endl;
|
|
|
|
//Instantiate NLP
|
|
NLP nlp;
|
|
nlp.cost.add();
|
|
|
|
// Instantiate SQP
|
|
SQPSimple sqpSimple(nlp);
|
|
}
|
|
|
|
//******************************************************************************
|
|
int main() {
|
|
TestResult tr;
|
|
return TestRegistry::runAllTests(tr);
|
|
}
|
|
//******************************************************************************
|
|
|
|
//TEST(testSQPSimple, Problem1 ) {
|
|
//
|
|
// // build a quadratic Objective function x1^2 - x1*x2 + x2^2 - 3*x1 + 5
|
|
// // Note the Hessian encodes:
|
|
// // 0.5*x1'*G11*x1 + x1'*G12*x2 + 0.5*x2'*G22*x2 - x1'*g1 - x2'*g2 + 0.5*f
|
|
// // Hence, we have G11=2, G12 = -1, g1 = +3, G22 = 2, g2 = 0, f = 10
|
|
// HessianFactor lf(X(1), X(2), 2.0 * ones(1, 1), -ones(1, 1), 3.0 * ones(1),
|
|
// 2.0 * ones(1, 1), zero(1), 10.0);
|
|
//
|
|
// // build linear inequalities
|
|
// LinearInequalityFactorGraph inequalities;
|
|
// inequalities.push_back(
|
|
// LinearInequality(X(1), ones(1, 1), X(2), ones(1, 1), 2, 0)); // x1 + x2 <= 2 --> x1 + x2 -2 <= 0, --> b=2
|
|
// inequalities.push_back(LinearInequality(X(1), -ones(1, 1), 0, 1)); // -x1 <= 0
|
|
// inequalities.push_back(LinearInequality(X(2), -ones(1, 1), 0, 2)); // -x2 <= 0
|
|
// inequalities.push_back(LinearInequality(X(1), ones(1, 1), 1.5, 3)); // x1 <= 3/2
|
|
//
|
|
// // Compare against a QP
|
|
// QP qp;
|
|
// qp.cost.add(lf);
|
|
// qp.inequalities = inequalities;
|
|
//
|
|
// // instantiate QPsolver
|
|
// QPSolver qpSolver(qp);
|
|
// // create initial values for optimization
|
|
// VectorValues initialVectorValues;
|
|
// initialVectorValues.insert(X(1), zero(1));
|
|
// initialVectorValues.insert(X(2), zero(1));
|
|
// VectorValues expectedSolution = qpSolver.optimize(initialVectorValues).first;
|
|
//
|
|
//
|
|
// NonlinearEqualityFactorGraph linearEqualities;
|
|
// NonlinearEqualityFactorGraph nonlinearEqualities;
|
|
// nonlinearEqualities.push_back(NonlinearEquality(X(1), ones(1, 1), X(2), ones(1, 1), 2, 0)));
|
|
//
|
|
// NLP nlp;
|
|
// nlp.cost.add(lf);
|
|
// nlp.linearEqualities.push_back(NonlinearEqualityFactorGraph());
|
|
// // instantiate QPsolver
|
|
// SQPSimple sqpSolver(nlp);
|
|
// // create initial values for optimization
|
|
// Values initialValues;
|
|
// initialValues.insert(X(1), zero(1));
|
|
// initialValues.insert(X(2), zero(1));
|
|
//
|
|
// std::pair<Vector, VectorValues> actualSolution = sqpSolver.optimize(initialValues);
|
|
//
|
|
// DOUBLES_EQUAL(expectedSolution.at(X(1))[0], actualSolution.at<double>(X(1)),
|
|
// tol);
|
|
// DOUBLES_EQUAL(expectedSolution.at(X(2))[0], actualSolution.at<double>(X(2)),
|
|
// tol);
|
|
//}
|