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Some refactoring, small edits, TODOs for Ivan

release/4.3a0
Frank Dellaert 2016-01-29 09:07:14 -08:00
parent 0af87e7298
commit 26a7647629
8 changed files with 262 additions and 259 deletions
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171
gtsam_unstable/linear/ActiveSetSolver.h
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@ -2,6 +2,7 @@
* @file ActiveSetSolver.h
* @brief Abstract class above for solving problems with the abstract set method.
* @author Ivan Dario Jimenez
* @author Duy Nguyen Ta
* @date 1/25/16
*/
#pragma once
@ -11,78 +12,39 @@
namespace gtsam {
class ActiveSetSolver {
protected:
public:
typedef std::vector<std::pair<Key, Matrix> > TermsContainer;
protected:
KeySet constrainedKeys_; //!< all constrained keys, will become factors in dual graphs
GaussianFactorGraph baseGraph_; //!< factor graphs of cost factors and linear equalities.
//!< used to initialize the working set factor graph,
//!< to which active inequalities will be added
VariableIndex costVariableIndex_, equalityVariableIndex_,
inequalityVariableIndex_; //!< index to corresponding factors to build dual graphs
ActiveSetSolver() :
constrainedKeys_() {
}
/**
* Compute step size alpha for the new solution x' = xk + alpha*p, where alpha \in [0,1]
*
* @return a tuple of (alpha, factorIndex, sigmaIndex) where (factorIndex, sigmaIndex)
* is the constraint that has minimum alpha, or (-1,-1) if alpha = 1.
* This constraint will be added to the working set and become active
* in the next iteration
*/
boost::tuple<double, int> computeStepSize(
const InequalityFactorGraph& workingSet, const VectorValues& xk,
const VectorValues& p, const double& startAlpha) const {
double minAlpha = startAlpha;
int closestFactorIx = -1;
for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
double b = factor->getb()[0];
// only check inactive factors
if (!factor->active()) {
// Compute a'*p
double aTp = factor->dotProductRow(p);
// Check if a'*p >0. Don't care if it's not.
if (aTp <= 0)
continue;
// Compute a'*xk
double aTx = factor->dotProductRow(xk);
// alpha = (b - a'*xk) / (a'*p)
double alpha = (b - aTx) / aTp;
// We want the minimum of all those max alphas
if (alpha < minAlpha) {
closestFactorIx = factorIx;
minAlpha = alpha;
}
}
}
return boost::make_tuple(minAlpha, closestFactorIx);
}
public:
/// Create a dual factor
virtual JacobianFactor::shared_ptr createDualFactor(Key key,
const InequalityFactorGraph& workingSet,
const VectorValues& delta) const = 0;
//******************************************************************************
/// Collect the Jacobian terms for a dual factor
template<typename FACTOR>
TermsContainer collectDualJacobians(Key key, const FactorGraph<FACTOR> &graph,
const VariableIndex &variableIndex) const {
/// Collect the Jacobian terms for a dual factor
template <typename FACTOR>
TermsContainer collectDualJacobians(
Key key, const FactorGraph<FACTOR>& graph,
const VariableIndex& variableIndex) const {
TermsContainer Aterms;
if (variableIndex.find(key) != variableIndex.end()) {
BOOST_FOREACH(size_t factorIx, variableIndex[key]) {
typename FACTOR::shared_ptr factor = graph.at(factorIx);
if (!factor->active()) continue;
Matrix Ai = factor->getA(factor->find(key)).transpose();
Aterms.push_back(std::make_pair(factor->dualKey(), Ai));
BOOST_FOREACH (size_t factorIx, variableIndex[key]) {
typename FACTOR::shared_ptr factor = graph.at(factorIx);
if (!factor->active()) continue;
Matrix Ai = factor->getA(factor->find(key)).transpose();
Aterms.push_back(std::make_pair(factor->dualKey(), Ai));
}
}
return Aterms;
}
return Aterms;
}
/**
* The goal of this function is to find currently active inequality constraints
@ -118,36 +80,83 @@ public:
* And we want to remove the worst one with the largest lambda from the active set.
*
*/
int identifyLeavingConstraint(const InequalityFactorGraph& workingSet,
const VectorValues& lambdas) const {
int worstFactorIx = -1;
// preset the maxLambda to 0.0: if lambda is <= 0.0, the constraint is either
// inactive or a good inequality constraint, so we don't care!
double maxLambda = 0.0;
for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
if (factor->active()) {
double lambda = lambdas.at(factor->dualKey())[0];
if (lambda > maxLambda) {
worstFactorIx = factorIx;
maxLambda = lambda;
int identifyLeavingConstraint(const InequalityFactorGraph& workingSet,
const VectorValues& lambdas) const {
int worstFactorIx = -1;
// preset the maxLambda to 0.0: if lambda is <= 0.0, the constraint is
// either
// inactive or a good inequality constraint, so we don't care!
double maxLambda = 0.0;
for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
if (factor->active()) {
double lambda = lambdas.at(factor->dualKey())[0];
if (lambda > maxLambda) {
worstFactorIx = factorIx;
maxLambda = lambda;
}
}
}
return worstFactorIx;
}
return worstFactorIx;
}
//******************************************************************************
GaussianFactorGraph::shared_ptr buildDualGraph(
const InequalityFactorGraph& workingSet, const VectorValues& delta) const {
GaussianFactorGraph::shared_ptr dualGraph(new GaussianFactorGraph());
BOOST_FOREACH(Key key, constrainedKeys_) {
// Each constrained key becomes a factor in the dual graph
JacobianFactor::shared_ptr dualFactor = createDualFactor(key, workingSet,
delta);
if (!dualFactor->empty()) dualGraph->push_back(dualFactor);
/// TODO: comment
GaussianFactorGraph::shared_ptr buildDualGraph(
const InequalityFactorGraph& workingSet,
const VectorValues& delta) const {
GaussianFactorGraph::shared_ptr dualGraph(new GaussianFactorGraph());
BOOST_FOREACH (Key key, constrainedKeys_) {
// Each constrained key becomes a factor in the dual graph
JacobianFactor::shared_ptr dualFactor =
createDualFactor(key, workingSet, delta);
if (!dualFactor->empty()) dualGraph->push_back(dualFactor);
}
return dualGraph;
}
return dualGraph;
}
protected:
ActiveSetSolver() : constrainedKeys_() {}
/**
* Compute step size alpha for the new solution x' = xk + alpha*p, where alpha \in [0,1]
*
* @return a tuple of (alpha, factorIndex, sigmaIndex) where (factorIndex, sigmaIndex)
* is the constraint that has minimum alpha, or (-1,-1) if alpha = 1.
* This constraint will be added to the working set and become active
* in the next iteration.
*/
boost::tuple<double, int> computeStepSize(
const InequalityFactorGraph& workingSet, const VectorValues& xk,
const VectorValues& p, const double& startAlpha) const {
double minAlpha = startAlpha;
int closestFactorIx = -1;
for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
double b = factor->getb()[0];
// only check inactive factors
if (!factor->active()) {
// Compute a'*p
double aTp = factor->dotProductRow(p);
// Check if a'*p >0. Don't care if it's not.
if (aTp <= 0)
continue;
// Compute a'*xk
double aTx = factor->dotProductRow(xk);
// alpha = (b - a'*xk) / (a'*p)
double alpha = (b - aTx) / aTp;
// We want the minimum of all those max alphas
if (alpha < minAlpha) {
closestFactorIx = factorIx;
minAlpha = alpha;
}
}
}
return boost::make_tuple(minAlpha, closestFactorIx);
}
};
}
} // namespace gtsam

3
gtsam_unstable/linear/InequalityFactorGraph.h
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@ -18,8 +18,9 @@
#pragma once
#include <gtsam/inference/FactorGraph.h>
#include <gtsam_unstable/linear/LinearInequality.h>
#include <gtsam/linear/VectorValues.h>
#include <gtsam/inference/FactorGraph.h>
namespace gtsam {

109
gtsam_unstable/linear/LPSolver.cpp
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@ -6,24 +6,24 @@
*/
#include <gtsam_unstable/linear/LPSolver.h>
#include <gtsam/linear/GaussianFactorGraph.h>
#include <gtsam_unstable/linear/InfeasibleInitialValues.h>
#include <gtsam/linear/GaussianFactorGraph.h>
namespace gtsam {
LPSolver::LPSolver(const LP &lp) :
lp_(lp) {
LPSolver::LPSolver(const LP &lp) : lp_(lp) {
// Push back factors that are the same in every iteration to the base graph.
// Those include the equality constraints and zero priors for keys that are not
// in the cost
// Those include the equality constraints and zero priors for keys that are
// not in the cost
baseGraph_.push_back(lp_.equalities);
// Collect key-dim map of all variables in the constraints to create their zero priors later
// Collect key-dim map of all variables in the constraints to create their
// zero priors later
keysDim_ = collectKeysDim(lp_.equalities);
KeyDimMap keysDim2 = collectKeysDim(lp_.inequalities);
keysDim_.insert(keysDim2.begin(), keysDim2.end());
// Create and push zero priors of constrained variables that do not exist in the cost function
// Create and push zero priors of constrained variables that do not exist in
// the cost function
baseGraph_.push_back(*createZeroPriors(lp_.cost.keys(), keysDim_));
// Variable index
@ -36,7 +36,7 @@ LPSolver::LPSolver(const LP &lp) :
GaussianFactorGraph::shared_ptr LPSolver::createZeroPriors(
const KeyVector &costKeys, const KeyDimMap &keysDim) const {
GaussianFactorGraph::shared_ptr graph(new GaussianFactorGraph());
BOOST_FOREACH(Key key, keysDim | boost::adaptors::map_keys) {
for (Key key: keysDim | boost::adaptors::map_keys) {
if (find(costKeys.begin(), costKeys.end(), key) == costKeys.end()) {
size_t dim = keysDim.at(key);
graph->push_back(JacobianFactor(key, eye(dim), zero(dim)));
@ -47,35 +47,36 @@ GaussianFactorGraph::shared_ptr LPSolver::createZeroPriors(
LPState LPSolver::iterate(const LPState &state) const {
// Solve with the current working set
// LP: project the objective neggradient to the constraint's null space
// LP: project the objective neg. gradient to the constraint's null space
// to find the direction to move
VectorValues newValues = solveWithCurrentWorkingSet(state.values,
state.workingSet);
VectorValues newValues =
solveWithCurrentWorkingSet(state.values, state.workingSet);
// If we CAN'T move further
// LP: projection on the constraints' nullspace is zero: we are at a vertex
if (newValues.equals(state.values, 1e-7)) {
// Find and remove the bad ineq constraint by computing its lambda
// Find and remove the bad inequality constraint by computing its lambda
// Compute lambda from the dual graph
// LP: project the objective's gradient onto each constraint gradient to obtain the dual scaling factors
// LP: project the objective's gradient onto each constraint gradient to
// obtain the dual scaling factors
// is it true??
GaussianFactorGraph::shared_ptr dualGraph = buildDualGraph(state.workingSet,
newValues);
GaussianFactorGraph::shared_ptr dualGraph =
buildDualGraph(state.workingSet, newValues);
VectorValues duals = dualGraph->optimize();
// LP: see which ineq constraint has wrong pulling direction, i.e., dual < 0
// LP: see which inequality constraint has wrong pulling direction, i.e., dual < 0
int leavingFactor = identifyLeavingConstraint(state.workingSet, duals);
// If all inequality constraints are satisfied: We have the solution!!
if (leavingFactor < 0) {
// TODO If we still have infeasible equality constraints: the problem is over-constrained. No solution!
// TODO If we still have infeasible equality constraints: the problem is
// over-constrained. No solution!
// ...
return LPState(newValues, duals, state.workingSet, true,
state.iterations + 1);
return LPState(newValues, duals, state.workingSet, true, state.iterations + 1);
} else {
// Inactivate the leaving constraint
// LP: remove the bad ineq constraint out of the working set
InequalityFactorGraph newWorkingSet = state.workingSet;
newWorkingSet.at(leavingFactor)->inactivate();
return LPState(newValues, duals, newWorkingSet, false,
state.iterations + 1);
return LPState(newValues, duals, newWorkingSet, false, state.iterations + 1);
}
} else {
// If we CAN make some progress, i.e. p_k != 0
@ -86,16 +87,14 @@ LPState LPSolver::iterate(const LPState &state) const {
double alpha;
int factorIx;
VectorValues p = newValues - state.values;
boost::tie(alpha, factorIx) = // using 16.41
boost::tie(alpha, factorIx) = // using 16.41
computeStepSize(state.workingSet, state.values, p);
// also add to the working set the one that complains the most
InequalityFactorGraph newWorkingSet = state.workingSet;
if (factorIx >= 0)
newWorkingSet.at(factorIx)->activate();
if (factorIx >= 0) newWorkingSet.at(factorIx)->activate();
// step!
newValues = state.values + alpha * p;
return LPState(newValues, state.duals, newWorkingSet, false,
state.iterations + 1);
return LPState(newValues, state.duals, newWorkingSet, false, state.iterations + 1);
}
}
@ -114,37 +113,35 @@ GaussianFactorGraph::shared_ptr LPSolver::createLeastSquareFactors(
}
VectorValues LPSolver::solveWithCurrentWorkingSet(
const VectorValues &xk,
const InequalityFactorGraph &workingSet) const {
GaussianFactorGraph workingGraph = baseGraph_; // || X - Xk + g ||^2
const VectorValues &xk, const InequalityFactorGraph &workingSet) const {
GaussianFactorGraph workingGraph = baseGraph_; // || X - Xk + g ||^2
workingGraph.push_back(*createLeastSquareFactors(lp_.cost, xk));
BOOST_FOREACH(const LinearInequality::shared_ptr& factor, workingSet) {
for (const LinearInequality::shared_ptr &factor: workingSet) {
if (factor->active()) workingGraph.push_back(factor);
}
return workingGraph.optimize();
}
boost::shared_ptr<JacobianFactor> LPSolver::createDualFactor(
Key key,
const InequalityFactorGraph &workingSet,
Key key, const InequalityFactorGraph &workingSet,
const VectorValues &delta) const {
// Transpose the A matrix of constrained factors to have the jacobian of the dual key
TermsContainer Aterms = collectDualJacobians < LinearEquality
> (key, lp_.equalities, equalityVariableIndex_);
TermsContainer AtermsInequalities = collectDualJacobians < LinearInequality
> (key, workingSet, inequalityVariableIndex_);
// Transpose the A matrix of constrained factors to have the jacobian of the
// dual key
TermsContainer Aterms = collectDualJacobians<LinearEquality>(
key, lp_.equalities, equalityVariableIndex_);
TermsContainer AtermsInequalities = collectDualJacobians<LinearInequality>(
key, workingSet, inequalityVariableIndex_);
Aterms.insert(Aterms.end(), AtermsInequalities.begin(),
AtermsInequalities.end());
AtermsInequalities.end());
// Collect the gradients of unconstrained cost factors to the b vector
if (Aterms.size() > 0) {
Vector b = zero(delta.at(key).size());
Factor::const_iterator it = lp_.cost.find(key);
if (it != lp_.cost.end())
b = lp_.cost.getA(it).transpose();
return boost::make_shared < JacobianFactor > (Aterms, b); // compute the least-square approximation of dual variables
if (it != lp_.cost.end()) b = lp_.cost.getA(it).transpose();
return boost::make_shared<JacobianFactor>(
Aterms, b); // compute the least-square approximation of dual variables
} else {
return boost::make_shared<JacobianFactor>();
}
@ -152,10 +149,9 @@ boost::shared_ptr<JacobianFactor> LPSolver::createDualFactor(
InequalityFactorGraph LPSolver::identifyActiveConstraints(
const InequalityFactorGraph &inequalities,
const VectorValues &initialValues,
const VectorValues &duals) const {
const VectorValues &initialValues, const VectorValues &duals) const {
InequalityFactorGraph workingSet;
BOOST_FOREACH(const LinearInequality::shared_ptr& factor, inequalities) {
for (const LinearInequality::shared_ptr &factor : inequalities) {
LinearInequality::shared_ptr workingFactor(new LinearInequality(*factor));
double error = workingFactor->error(initialValues);
@ -165,8 +161,7 @@ InequalityFactorGraph LPSolver::identifyActiveConstraints(
if (fabs(error) < 1e-7) {
workingFactor->activate();
}
else {
} else {
workingFactor->inactivate();
}
workingSet.push_back(workingFactor);
@ -175,29 +170,25 @@ InequalityFactorGraph LPSolver::identifyActiveConstraints(
}
std::pair<VectorValues, VectorValues> LPSolver::optimize(
const VectorValues &initialValues,
const VectorValues &duals) const {
const VectorValues &initialValues, const VectorValues &duals) const {
{
// Initialize workingSet from the feasible initialValues
InequalityFactorGraph workingSet = identifyActiveConstraints(
lp_.inequalities, initialValues, duals);
InequalityFactorGraph workingSet =
identifyActiveConstraints(lp_.inequalities, initialValues, duals);
LPState state(initialValues, duals, workingSet, false, 0);
/// main loop of the solver
while (!state.converged) {
while (!state.converged)
state = iterate(state);
}
return make_pair(state.values, state.duals);
}
}
boost::tuples::tuple<double, int> LPSolver::computeStepSize(
const InequalityFactorGraph &workingSet,
const VectorValues &xk,
const InequalityFactorGraph &workingSet, const VectorValues &xk,
const VectorValues &p) const {
return ActiveSetSolver::computeStepSize(workingSet, xk, p,
std::numeric_limits<double>::infinity());
return ActiveSetSolver::computeStepSize(
workingSet, xk, p, std::numeric_limits<double>::infinity());
}
}

26
gtsam_unstable/linear/LPSolver.h
View File

@ -2,6 +2,7 @@
* @file LPSolver.h
* @brief Class used to solve Linear Programming Problems as defined in LP.h
* @author Ivan Dario Jimenez
* @author Duy Nguyen Ta
* @date 1/24/16
*/
@ -10,9 +11,10 @@
#include <gtsam_unstable/linear/LPState.h>
#include <gtsam_unstable/linear/LP.h>
#include <gtsam_unstable/linear/ActiveSetSolver.h>
#include <boost/range/adaptor/map.hpp>
#include <gtsam/linear/VectorValues.h>
#include <boost/range/adaptor/map.hpp>
namespace gtsam {
typedef std::map<Key, size_t> KeyDimMap;
@ -28,11 +30,12 @@ public:
const LP& lp() const {
return lp_;
}
const KeyDimMap& keysDim() const {
return keysDim_;
}
//******************************************************************************
/// TODO(comment)
template<class LinearGraph>
KeyDimMap collectKeysDim(const LinearGraph& linearGraph) const {
KeyDimMap keysDim;
@ -44,17 +47,13 @@ public:
return keysDim;
}
//******************************************************************************
/**
* Create a zero prior for any keys in the graph that don't exist in the cost
*/
/// Create a zero prior for any keys in the graph that don't exist in the cost
GaussianFactorGraph::shared_ptr createZeroPriors(const KeyVector& costKeys,
const KeyDimMap& keysDim) const;
//******************************************************************************
/// TODO(comment)
LPState iterate(const LPState& state) const;
//******************************************************************************
/**
* Create the factor ||x-xk - (-g)||^2 where xk is the current feasible solution
* on the constraint surface and g is the gradient of the linear cost,
@ -74,28 +73,27 @@ public:
VectorValues solveWithCurrentWorkingSet(const VectorValues& xk,
const InequalityFactorGraph& workingSet) const;
//******************************************************************************
/// TODO(comment)
JacobianFactor::shared_ptr createDualFactor(Key key,
const InequalityFactorGraph& workingSet, const VectorValues& delta) const;
//******************************************************************************
/// TODO(comment)
boost::tuple<double, int> computeStepSize(
const InequalityFactorGraph& workingSet, const VectorValues& xk,
const VectorValues& p) const;
//******************************************************************************
/// TODO(comment)
InequalityFactorGraph identifyActiveConstraints(
const InequalityFactorGraph& inequalities,
const VectorValues& initialValues, const VectorValues& duals) const;
//******************************************************************************
/** Optimize with the provided feasible initial values
* TODO: throw exception if the initial values is not feasible wrt inequality constraints
* TODO: comment duals
*/
pair<VectorValues, VectorValues> optimize(const VectorValues& initialValues,
const VectorValues& duals = VectorValues()) const;
//******************************************************************************
/**
* Optimize without initial values
* TODO: Find a feasible initial solution wrt inequality constraints
@ -115,4 +113,4 @@ public:
// return make_pair(state.values, state.duals);
// }
};
}
} // namespace gtsam

2
gtsam_unstable/linear/LPState.h
View File

@ -10,7 +10,9 @@
namespace gtsam {
// TODO: comment
struct LPState {
// TODO: comment member variables
VectorValues values;
VectorValues duals;
InequalityFactorGraph workingSet;

1
gtsam_unstable/linear/LinearInequality.h
View File

@ -19,6 +19,7 @@
#pragma once
#include <gtsam/linear/JacobianFactor.h>
#include <gtsam/linear/VectorValues.h>
namespace gtsam {

192
gtsam_unstable/linear/QPSolver.cpp
View File

@ -27,8 +27,7 @@ using namespace std;
namespace gtsam {
//******************************************************************************
QPSolver::QPSolver(const QP& qp) :
qp_(qp) {
QPSolver::QPSolver(const QP& qp) : qp_(qp) {
baseGraph_ = qp_.cost;
baseGraph_.push_back(qp_.equalities.begin(), qp_.equalities.end());
costVariableIndex_ = VariableIndex(qp_.cost);
@ -42,39 +41,41 @@ QPSolver::QPSolver(const QP& qp) :
VectorValues QPSolver::solveWithCurrentWorkingSet(
const InequalityFactorGraph& workingSet) const {
GaussianFactorGraph workingGraph = baseGraph_;
BOOST_FOREACH(const LinearInequality::shared_ptr& factor, workingSet) {
if (factor->active())
workingGraph.push_back(factor);
for (const LinearInequality::shared_ptr& factor : workingSet) {
if (factor->active()) workingGraph.push_back(factor);
}
return workingGraph.optimize();
}
//******************************************************************************
JacobianFactor::shared_ptr QPSolver::createDualFactor(Key key,
const InequalityFactorGraph& workingSet, const VectorValues& delta) const {
// Transpose the A matrix of constrained factors to have the jacobian of the dual key
std::vector < std::pair<Key, Matrix> > Aterms = collectDualJacobians
< LinearEquality > (key, qp_.equalities, equalityVariableIndex_);
std::vector < std::pair<Key, Matrix> > AtermsInequalities =
collectDualJacobians < LinearInequality
> (key, workingSet, inequalityVariableIndex_);
JacobianFactor::shared_ptr QPSolver::createDualFactor(
Key key, const InequalityFactorGraph& workingSet,
const VectorValues& delta) const {
// Transpose the A matrix of constrained factors to have the jacobian of the
// dual key
std::vector<std::pair<Key, Matrix> > Aterms =
collectDualJacobians<LinearEquality>(key, qp_.equalities,
equalityVariableIndex_);
std::vector<std::pair<Key, Matrix> > AtermsInequalities =
collectDualJacobians<LinearInequality>(key, workingSet,
inequalityVariableIndex_);
Aterms.insert(Aterms.end(), AtermsInequalities.begin(),
AtermsInequalities.end());
AtermsInequalities.end());
// Collect the gradients of unconstrained cost factors to the b vector
if (Aterms.size() > 0) {
Vector b = zero(delta.at(key).size());
if (costVariableIndex_.find(key) != costVariableIndex_.end()) {
BOOST_FOREACH(size_t factorIx, costVariableIndex_[key]) {
GaussianFactor::shared_ptr factor = qp_.cost.at(factorIx);
b += factor->gradient(key, delta);
for (size_t factorIx: costVariableIndex_[key]) {
GaussianFactor::shared_ptr factor = qp_.cost.at(factorIx);
b += factor->gradient(key, delta);
}
}
return boost::make_shared<JacobianFactor>(
Aterms, b); // compute the least-square approximation of dual variables
} else {
return boost::make_shared<JacobianFactor>();
}
return boost::make_shared < JacobianFactor > (Aterms, b); // compute the least-square approximation of dual variables
} else {
return boost::make_shared<JacobianFactor>();
}
}
//******************************************************************************
@ -94,102 +95,101 @@ JacobianFactor::shared_ptr QPSolver::createDualFactor(Key key,
* We want the minimum of all those alphas among all inactive inequality.
*/
boost::tuple<double, int> QPSolver::computeStepSize(
const InequalityFactorGraph& workingSet, const VectorValues& xk,
const VectorValues& p) const {
return ActiveSetSolver::computeStepSize(workingSet, xk, p, 1);
const InequalityFactorGraph& workingSet, const VectorValues& xk,
const VectorValues& p) const {
return ActiveSetSolver::computeStepSize(workingSet, xk, p, 1);
}
//******************************************************************************
QPState QPSolver::iterate(const QPState& state) const {
// Algorithm 16.3 from Nocedal06book.
// Solve with the current working set eqn 16.39, but instead of solving for p solve for x
VectorValues newValues = solveWithCurrentWorkingSet(state.workingSet);
// If we CAN'T move further
// if p_k = 0 is the original condition, modified by Duy to say that the state update is zero.
if (newValues.equals(state.values, 1e-7)) {
// Compute lambda from the dual graph
GaussianFactorGraph::shared_ptr dualGraph = buildDualGraph(state.workingSet,
newValues);
VectorValues duals = dualGraph->optimize();
int leavingFactor = identifyLeavingConstraint(state.workingSet, duals);
// If all inequality constraints are satisfied: We have the solution!!
if (leavingFactor < 0) {
return QPState(newValues, duals, state.workingSet, true,
state.iterations + 1);
// Algorithm 16.3 from Nocedal06book.
// Solve with the current working set eqn 16.39, but instead of solving for p
// solve for x
VectorValues newValues = solveWithCurrentWorkingSet(state.workingSet);
// If we CAN'T move further
// if p_k = 0 is the original condition, modified by Duy to say that the state
// update is zero.
if (newValues.equals(state.values, 1e-7)) {
// Compute lambda from the dual graph
GaussianFactorGraph::shared_ptr dualGraph =
buildDualGraph(state.workingSet, newValues);
VectorValues duals = dualGraph->optimize();
int leavingFactor = identifyLeavingConstraint(state.workingSet, duals);
// If all inequality constraints are satisfied: We have the solution!!
if (leavingFactor < 0) {
return QPState(newValues, duals, state.workingSet, true,
state.iterations + 1);
} else {
// Inactivate the leaving constraint
InequalityFactorGraph newWorkingSet = state.workingSet;
newWorkingSet.at(leavingFactor)->inactivate();
return QPState(newValues, duals, newWorkingSet, false,
state.iterations + 1);
}
} else {
// Inactivate the leaving constraint
// If we CAN make some progress, i.e. p_k != 0
// Adapt stepsize if some inactive constraints complain about this move
double alpha;
int factorIx;
VectorValues p = newValues - state.values;
boost::tie(alpha, factorIx) = // using 16.41
computeStepSize(state.workingSet, state.values, p);
// also add to the working set the one that complains the most
InequalityFactorGraph newWorkingSet = state.workingSet;
newWorkingSet.at(leavingFactor)->inactivate();
return QPState(newValues, duals, newWorkingSet, false, state.iterations + 1);
if (factorIx >= 0) newWorkingSet.at(factorIx)->activate();
// step!
newValues = state.values + alpha * p;
return QPState(newValues, state.duals, newWorkingSet, false,
state.iterations + 1);
}
} else {
// If we CAN make some progress, i.e. p_k != 0
// Adapt stepsize if some inactive constraints complain about this move
double alpha;
int factorIx;
VectorValues p = newValues - state.values;
boost::tie(alpha, factorIx) = // using 16.41
computeStepSize(state.workingSet, state.values, p);
// also add to the working set the one that complains the most
InequalityFactorGraph newWorkingSet = state.workingSet;
if (factorIx >= 0)
newWorkingSet.at(factorIx)->activate();
// step!
newValues = state.values + alpha * p;
return QPState(newValues, state.duals, newWorkingSet, false,
state.iterations + 1);
}
}
//******************************************************************************
InequalityFactorGraph QPSolver::identifyActiveConstraints(
const InequalityFactorGraph& inequalities, const VectorValues& initialValues,
const VectorValues& duals, bool useWarmStart) const {
InequalityFactorGraph workingSet;
BOOST_FOREACH(const LinearInequality::shared_ptr& factor, inequalities) {
LinearInequality::shared_ptr workingFactor(new LinearInequality(*factor));
if (useWarmStart == true && duals.exists(workingFactor->dualKey())) {
workingFactor->activate();
}
else {
if (useWarmStart == true && duals.size() > 0) {
workingFactor->inactivate();
const InequalityFactorGraph& inequalities,
const VectorValues& initialValues, const VectorValues& duals,
bool useWarmStart) const {
InequalityFactorGraph workingSet;
for (const LinearInequality::shared_ptr& factor: inequalities) {
LinearInequality::shared_ptr workingFactor(new LinearInequality(*factor));
if (useWarmStart == true && duals.exists(workingFactor->dualKey())) {
workingFactor->activate();
} else {
double error = workingFactor->error(initialValues);
// TODO: find a feasible initial point for QPSolver.
// For now, we just throw an exception, since we don't have an LPSolver to do this yet
if (error > 0)
throw InfeasibleInitialValues();
if (fabs(error)<1e-7) {
workingFactor->activate();
}
else {
if (useWarmStart == true && duals.size() > 0) {
workingFactor->inactivate();
} else {
double error = workingFactor->error(initialValues);
// TODO: find a feasible initial point for QPSolver.
// For now, we just throw an exception, since we don't have an LPSolver
// to do this yet
if (error > 0) throw InfeasibleInitialValues();
if (fabs(error) < 1e-7) {
workingFactor->activate();
} else {
workingFactor->inactivate();
}
}
}
workingSet.push_back(workingFactor);
}
workingSet.push_back(workingFactor);
}
return workingSet;
return workingSet;
}
//******************************************************************************
pair<VectorValues, VectorValues> QPSolver::optimize(
const VectorValues& initialValues, const VectorValues& duals,
bool useWarmStart) const {
const VectorValues& initialValues, const VectorValues& duals,
bool useWarmStart) const {
// Initialize workingSet from the feasible initialValues
InequalityFactorGraph workingSet = identifyActiveConstraints(
qp_.inequalities, initialValues, duals, useWarmStart);
QPState state(initialValues, duals, workingSet, false, 0);
// Initialize workingSet from the feasible initialValues
InequalityFactorGraph workingSet = identifyActiveConstraints(qp_.inequalities,
initialValues, duals, useWarmStart);
QPState state(initialValues, duals, workingSet, false, 0);
/// main loop of the solver
while (!state.converged)
state = iterate(state);
/// main loop of the solver
while (!state.converged) {
state = iterate(state);
}
return make_pair(state.values, state.duals);
return make_pair(state.values, state.duals);
}
} /* namespace gtsam */

17
gtsam_unstable/linear/QPSolver.h
View File

@ -13,20 +13,22 @@
* @file QPSolver.h
* @brief A quadratic programming solver implements the active set method
* @date Apr 15, 2014
* @author Ivan Dario Jimenez
* @author Duy-Nguyen Ta
*/
#pragma once
#include <gtsam/linear/VectorValues.h>
#include <gtsam_unstable/linear/QP.h>
#include <gtsam_unstable/linear/ActiveSetSolver.h>
#include <gtsam_unstable/linear/QPState.h>
#include <gtsam/linear/VectorValues.h>
#include <vector>
#include <set>
namespace gtsam {
/**
* This QPSolver uses the active set method to solve a quadratic programming problem
* defined in the QP struct.
@ -48,24 +50,23 @@ public:
/// Create a dual factor
JacobianFactor::shared_ptr createDualFactor(Key key,
const InequalityFactorGraph& workingSet, const VectorValues& delta) const;
/// @}
/// TODO(comment)
boost::tuple<double, int> computeStepSize(
const InequalityFactorGraph& workingSet, const VectorValues& xk,
const VectorValues& p) const;
/** Iterate 1 step, return a new state with a new workingSet and values */
/// Iterate 1 step, return a new state with a new workingSet and values
QPState iterate(const QPState& state) const;
/**
* Identify active constraints based on initial values.
*/
/// Identify active constraints based on initial values.
InequalityFactorGraph identifyActiveConstraints(
const InequalityFactorGraph& inequalities,
const VectorValues& initialValues, const VectorValues& duals =
VectorValues(), bool useWarmStart = true) const;
/** Optimize with a provided initial values
/**
* Optimize with provided initial values
* For this version, it is the responsibility of the caller to provide
* a feasible initial value, otherwise, an exception will be thrown.
* @return a pair of <primal, dual> solutions
@ -76,4 +77,4 @@ public:
};
} /* namespace gtsam */
} // namespace gtsam