[REFACTOR] Extracted LPInitSolver.h from testLPSolver.cpp
[REFACTOR] Extracted LPSolver.h from testLPSolver.cpp [REFACTOR] Extracted LPState.h from testLPSolver.cpprelease/4.3a0
ivan
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#pragma once
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namespace gtsam {
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/**
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* Abstract class to solve for an initial value of an LP problem
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*/
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class LPInitSolver {
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protected:
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const LP& lp_;
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const LPSolver& lpSolver_;
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public:
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LPInitSolver(const LPSolver& lpSolver) :
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lp_(lpSolver.lp()), lpSolver_(lpSolver) {
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}
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virtual ~LPInitSolver() {
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}
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;
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virtual VectorValues solve() const = 0;
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};
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}
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/**
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* @file LPSolver.h
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* @brief Class used to solve Linear Programming Problems as defined in LP.h
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* @author Ivan Dario Jimenez
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* @date 1/24/16
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*/
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#pragma once
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namespace gtsam {
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typedef std::map<Key, size_t> KeyDimMap;
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typedef std::vector<std::pair<Key, Matrix> > TermsContainer;
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class LPSolver {
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const LP& lp_; //!< the linear programming problem
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GaussianFactorGraph baseGraph_; //!< unchanged factors needed in every iteration
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VariableIndex costVariableIndex_, equalityVariableIndex_,
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inequalityVariableIndex_; //!< index to corresponding factors to build dual graphs
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FastSet<Key> constrainedKeys_; //!< all constrained keys, will become factors in dual graphs
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KeyDimMap keysDim_; //!< key-dim map of all variables in the constraints, used to create zero priors
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public:
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LPSolver(const LP& lp) :
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lp_(lp) {
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// Push back factors that are the same in every iteration to the base graph.
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// Those include the equality constraints and zero priors for keys that are not
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// in the cost
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baseGraph_.push_back(lp_.equalities);
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// Collect key-dim map of all variables in the constraints to create their zero priors later
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keysDim_ = collectKeysDim(lp_.equalities);
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KeyDimMap keysDim2 = collectKeysDim(lp_.inequalities);
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keysDim_.insert(keysDim2.begin(), keysDim2.end());
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// Create and push zero priors of constrained variables that do not exist in the cost function
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baseGraph_.push_back(*createZeroPriors(lp_.cost.keys(), keysDim_));
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// Variable index
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equalityVariableIndex_ = VariableIndex(lp_.equalities);
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inequalityVariableIndex_ = VariableIndex(lp_.inequalities);
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constrainedKeys_ = lp_.equalities.keys();
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constrainedKeys_.merge(lp_.inequalities.keys());
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}
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const LP& lp() const {
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return lp_;
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}
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const KeyDimMap& keysDim() const {
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return keysDim_;
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}
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//******************************************************************************
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template<class LinearGraph>
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KeyDimMap collectKeysDim(const LinearGraph& linearGraph) const {
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KeyDimMap keysDim;
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BOOST_FOREACH(const typename LinearGraph::sharedFactor& factor, linearGraph) {
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if (!factor) continue;
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BOOST_FOREACH(Key key, factor->keys())
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keysDim[key] = factor->getDim(factor->find(key));
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}
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return keysDim;
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}
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//******************************************************************************
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/**
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* Create a zero prior for any keys in the graph that don't exist in the cost
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*/
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GaussianFactorGraph::shared_ptr createZeroPriors(const KeyVector& costKeys,
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const KeyDimMap& keysDim) const {
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GaussianFactorGraph::shared_ptr graph(new GaussianFactorGraph());
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BOOST_FOREACH(Key key, keysDim | boost::adaptors::map_keys) {
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if (find(costKeys.begin(), costKeys.end(), key) == costKeys.end()) {
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size_t dim = keysDim.at(key);
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graph->push_back(JacobianFactor(key, eye(dim), zero(dim)));
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}
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}
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return graph;
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}
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//******************************************************************************
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LPState iterate(const LPState& state) const {
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static bool debug = false;
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// Solve with the current working set
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// LP: project the objective neggradient to the constraint's null space
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// to find the direction to move
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VectorValues newValues = solveWithCurrentWorkingSet(state.values,
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state.workingSet);
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// if (debug) state.workingSet.print("Working set:");
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if (debug)
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(newValues - state.values).print("New direction:");
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// If we CAN'T move further
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// LP: projection on the constraints' nullspace is zero: we are at a vertex
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if (newValues.equals(state.values, 1e-7)) {
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// Find and remove the bad ineq constraint by computing its lambda
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// Compute lambda from the dual graph
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// LP: project the objective's gradient onto each constraint gradient to obtain the dual scaling factors
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// is it true??
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if (debug)
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cout << "Building dual graph..." << endl;
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GaussianFactorGraph::shared_ptr dualGraph = buildDualGraph(
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state.workingSet, newValues);
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if (debug)
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dualGraph->print("Dual graph: ");
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VectorValues duals = dualGraph->optimize();
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if (debug)
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duals.print("Duals :");
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// LP: see which ineq constraint has wrong pulling direction, i.e., dual < 0
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int leavingFactor = identifyLeavingConstraint(state.workingSet, duals);
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if (debug)
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cout << "leavingFactor: " << leavingFactor << endl;
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// If all inequality constraints are satisfied: We have the solution!!
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if (leavingFactor < 0) {
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// TODO If we still have infeasible equality constraints: the problem is over-constrained. No solution!
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// ...
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return LPState(newValues, duals, state.workingSet, true,
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state.iterations + 1);
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} else {
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// Inactivate the leaving constraint
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// LP: remove the bad ineq constraint out of the working set
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InequalityFactorGraph newWorkingSet = state.workingSet;
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newWorkingSet.at(leavingFactor)->inactivate();
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return LPState(newValues, duals, newWorkingSet, false,
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state.iterations + 1);
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}
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} else {
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// If we CAN make some progress, i.e. p_k != 0
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// Adapt stepsize if some inactive constraints complain about this move
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// LP: projection on nullspace is NOT zero:
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// find and put a blocking inactive constraint to the working set,
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// otherwise the problem is unbounded!!!
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double alpha;
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int factorIx;
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VectorValues p = newValues - state.values;
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boost::tie(alpha, factorIx) = // using 16.41
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computeStepSize(state.workingSet, state.values, p);
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if (debug)
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cout << "alpha, factorIx: " << alpha << " " << factorIx << " " << endl;
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// also add to the working set the one that complains the most
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InequalityFactorGraph newWorkingSet = state.workingSet;
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if (factorIx >= 0)
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newWorkingSet.at(factorIx)->activate();
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// step!
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newValues = state.values + alpha * p;
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if (debug)
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newValues.print("New solution:");
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return LPState(newValues, state.duals, newWorkingSet, false,
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state.iterations + 1);
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}
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}
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//******************************************************************************
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/**
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* Create the factor ||x-xk - (-g)||^2 where xk is the current feasible solution
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* on the constraint surface and g is the gradient of the linear cost,
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* i.e. -g is the direction we wish to follow to decrease the cost.
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*
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* Essentially, we try to match the direction d = x-xk with -g as much as possible
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* subject to the condition that x needs to be on the constraint surface, i.e., d is
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* along the surface's subspace.
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*
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* The least-square solution of this quadratic subject to a set of linear constraints
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* is the projection of the gradient onto the constraints' subspace
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*/
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GaussianFactorGraph::shared_ptr createLeastSquareFactors(
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const LinearCost& cost, const VectorValues& xk) const {
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GaussianFactorGraph::shared_ptr graph(new GaussianFactorGraph());
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KeyVector keys = cost.keys();
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for (LinearCost::const_iterator it = cost.begin(); it != cost.end(); ++it) {
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size_t dim = cost.getDim(it);
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Vector b = xk.at(*it) - cost.getA(it).transpose(); // b = xk-g
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graph->push_back(JacobianFactor(*it, eye(dim), b));
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}
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return graph;
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}
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//******************************************************************************
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VectorValues solveWithCurrentWorkingSet(const VectorValues& xk,
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const InequalityFactorGraph& workingSet) const {
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GaussianFactorGraph workingGraph = baseGraph_; // || X - Xk + g ||^2
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workingGraph.push_back(*createLeastSquareFactors(lp_.cost, xk));
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BOOST_FOREACH(const LinearInequality::shared_ptr& factor, workingSet) {
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if (factor->active()) workingGraph.push_back(factor);
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}
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return workingGraph.optimize();
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}
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//******************************************************************************
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/// Collect the Jacobian terms for a dual factor
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template<typename FACTOR>
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TermsContainer collectDualJacobians(Key key, const FactorGraph<FACTOR>& graph,
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const VariableIndex& variableIndex) const {
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TermsContainer Aterms;
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if (variableIndex.find(key) != variableIndex.end()) {
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BOOST_FOREACH(size_t factorIx, variableIndex[key]) {
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typename FACTOR::shared_ptr factor = graph.at(factorIx);
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if (!factor->active()) continue;
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Matrix Ai = factor->getA(factor->find(key)).transpose();
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Aterms.push_back(std::make_pair(factor->dualKey(), Ai));
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}
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}
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return Aterms;
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}
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//******************************************************************************
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JacobianFactor::shared_ptr createDualFactor(Key key,
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const InequalityFactorGraph& workingSet, const VectorValues& delta) const {
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// Transpose the A matrix of constrained factors to have the jacobian of the dual key
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TermsContainer Aterms = collectDualJacobians<LinearEquality>(key,
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lp_.equalities, equalityVariableIndex_);
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TermsContainer AtermsInequalities = collectDualJacobians<LinearInequality>(
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key, workingSet, inequalityVariableIndex_);
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Aterms.insert(Aterms.end(), AtermsInequalities.begin(),
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AtermsInequalities.end());
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// Collect the gradients of unconstrained cost factors to the b vector
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if (Aterms.size() > 0) {
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Vector b = zero(delta.at(key).size());
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Factor::const_iterator it = lp_.cost.find(key);
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if (it != lp_.cost.end())
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b = lp_.cost.getA(it).transpose();
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return boost::make_shared < JacobianFactor > (Aterms, b); // compute the least-square approximation of dual variables
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} else {
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return boost::make_shared<JacobianFactor>();
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}
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}
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//******************************************************************************
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GaussianFactorGraph::shared_ptr buildDualGraph(
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const InequalityFactorGraph& workingSet, const VectorValues& delta) const {
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GaussianFactorGraph::shared_ptr dualGraph(new GaussianFactorGraph());
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BOOST_FOREACH(Key key, constrainedKeys_) {
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// Each constrained key becomes a factor in the dual graph
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JacobianFactor::shared_ptr dualFactor = createDualFactor(key, workingSet,
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delta);
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if (!dualFactor->empty()) dualGraph->push_back(dualFactor);
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}
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return dualGraph;
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}
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//******************************************************************************
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int identifyLeavingConstraint(const InequalityFactorGraph& workingSet,
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const VectorValues& duals) const {
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int worstFactorIx = -1;
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// preset the maxLambda to 0.0: if lambda is <= 0.0, the constraint is either
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// inactive or a good inequality constraint, so we don't care!
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double max_s = 0.0;
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for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
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const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
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if (factor->active()) {
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double s = duals.at(factor->dualKey())[0];
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if (s > max_s) {
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worstFactorIx = factorIx;
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max_s = s;
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}
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}
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}
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return worstFactorIx;
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}
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//******************************************************************************
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std::pair<double, int> computeStepSize(const InequalityFactorGraph& workingSet,
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const VectorValues& xk, const VectorValues& p) const {
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static bool debug = false;
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double minAlpha = std::numeric_limits<double>::infinity();
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int closestFactorIx = -1;
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for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
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const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
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double b = factor->getb()[0];
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// only check inactive factors
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if (!factor->active()) {
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// Compute a'*p
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double aTp = factor->dotProductRow(p);
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// Check if a'*p >0. Don't care if it's not.
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if (aTp <= 0)
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continue;
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// Compute a'*xk
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double aTx = factor->dotProductRow(xk);
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// alpha = (b - a'*xk) / (a'*p)
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double alpha = (b - aTx) / aTp;
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if (debug)
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cout << "alpha: " << alpha << endl;
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// We want the minimum of all those max alphas
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if (alpha < minAlpha) {
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closestFactorIx = factorIx;
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minAlpha = alpha;
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}
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}
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}
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return std::make_pair(minAlpha, closestFactorIx);
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}
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//******************************************************************************
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InequalityFactorGraph identifyActiveConstraints(
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const InequalityFactorGraph& inequalities,
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const VectorValues& initialValues, const VectorValues& duals) const {
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InequalityFactorGraph workingSet;
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BOOST_FOREACH(const LinearInequality::shared_ptr& factor, inequalities) {
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LinearInequality::shared_ptr workingFactor(new LinearInequality(*factor));
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double error = workingFactor->error(initialValues);
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// TODO: find a feasible initial point for LPSolver.
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// For now, we just throw an exception
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if (error > 0) throw InfeasibleInitialValues();
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if (fabs(error) < 1e-7) {
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workingFactor->activate();
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}
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else {
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workingFactor->inactivate();
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}
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workingSet.push_back(workingFactor);
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}
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return workingSet;
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}
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//******************************************************************************
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/** Optimize with the provided feasible initial values
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* TODO: throw exception if the initial values is not feasible wrt inequality constraints
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*/
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pair<VectorValues, VectorValues> optimize(const VectorValues& initialValues,
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const VectorValues& duals = VectorValues()) const {
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// Initialize workingSet from the feasible initialValues
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InequalityFactorGraph workingSet = identifyActiveConstraints(lp_.inequalities,
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initialValues, duals);
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LPState state(initialValues, duals, workingSet, false, 0);
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/// main loop of the solver
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while (!state.converged) {
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state = iterate(state);
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}
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return make_pair(state.values, state.duals);
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}
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//******************************************************************************
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/**
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* Optimize without initial values
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* TODO: Find a feasible initial solution wrt inequality constraints
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*/
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// pair<VectorValues, VectorValues> optimize() const {
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//
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// // Initialize workingSet from the feasible initialValues
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// InequalityFactorGraph workingSet = identifyActiveConstraints(
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// lp_.inequalities, initialValues, duals);
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// LPState state(initialValues, duals, workingSet, false, 0);
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//
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// /// main loop of the solver
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// while (!state.converged) {
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// state = iterate(state);
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// }
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//
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// return make_pair(state.values, state.duals);
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// }
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};
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}
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@ -5,8 +5,6 @@
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* @date 1/24/16
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*/
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namespace gtsam {
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struct LPState {
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@ -18,16 +16,16 @@ struct LPState {
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/// default constructor
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LPState() :
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values(), duals(), workingSet(), converged(false), iterations(0) {
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values(), duals(), workingSet(), converged(false), iterations(0) {
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}
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/// constructor with initial values
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LPState(const VectorValues& initialValues, const VectorValues& initialDuals,
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const InequalityFactorGraph& initialWorkingSet, bool _converged,
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size_t _iterations) :
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values(initialValues), duals(initialDuals), workingSet(initialWorkingSet), converged(
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_converged), iterations(_iterations) {
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const InequalityFactorGraph& initialWorkingSet, bool _converged,
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size_t _iterations) :
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values(initialValues), duals(initialDuals), workingSet(initialWorkingSet), converged(
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_converged), iterations(_iterations) {
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}
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};
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}
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}
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#include <boost/foreach.hpp>
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#include <boost/range/adaptor/map.hpp>
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#include <gtsam_unstable/linear/InfeasibleInitialValues.h>
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#include <gtsam_unstable/linear/InfeasibleOrUnboundedProblem.h>
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#include <gtsam_unstable/linear/LP.h>
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#include <gtsam_unstable/linear/LPState.h>
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#include <gtsam_unstable/linear/LPSolver.h>
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#include <gtsam_unstable/linear/InfeasibleOrUnboundedProblem.h>
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#include <gtsam_unstable/linear/LPInitSolver.h>
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using namespace std;
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using namespace gtsam;
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@ -40,380 +41,6 @@ using namespace gtsam::symbol_shorthand;
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namespace gtsam {
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typedef std::map<Key, size_t> KeyDimMap;
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typedef std::vector<std::pair<Key, Matrix> > TermsContainer;
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class LPSolver {
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const LP& lp_; //!< the linear programming problem
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GaussianFactorGraph baseGraph_; //!< unchanged factors needed in every iteration
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VariableIndex costVariableIndex_, equalityVariableIndex_,
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inequalityVariableIndex_; //!< index to corresponding factors to build dual graphs
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FastSet<Key> constrainedKeys_; //!< all constrained keys, will become factors in dual graphs
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KeyDimMap keysDim_; //!< key-dim map of all variables in the constraints, used to create zero priors
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public:
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LPSolver(const LP& lp) :
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lp_(lp) {
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// Push back factors that are the same in every iteration to the base graph.
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// Those include the equality constraints and zero priors for keys that are not
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// in the cost
|
||||
baseGraph_.push_back(lp_.equalities);
|
||||
|
||||
// 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
|
||||
baseGraph_.push_back(*createZeroPriors(lp_.cost.keys(), keysDim_));
|
||||
|
||||
// Variable index
|
||||
equalityVariableIndex_ = VariableIndex(lp_.equalities);
|
||||
inequalityVariableIndex_ = VariableIndex(lp_.inequalities);
|
||||
constrainedKeys_ = lp_.equalities.keys();
|
||||
constrainedKeys_.merge(lp_.inequalities.keys());
|
||||
}
|
||||
|
||||
const LP& lp() const { return lp_; }
|
||||
const KeyDimMap& keysDim() const { return keysDim_; }
|
||||
|
||||
//******************************************************************************
|
||||
template<class LinearGraph>
|
||||
KeyDimMap collectKeysDim(const LinearGraph& linearGraph) const {
|
||||
KeyDimMap keysDim;
|
||||
BOOST_FOREACH(const typename LinearGraph::sharedFactor& factor, linearGraph) {
|
||||
if (!factor) continue;
|
||||
BOOST_FOREACH(Key key, factor->keys())
|
||||
keysDim[key] = factor->getDim(factor->find(key));
|
||||
}
|
||||
return keysDim;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
/**
|
||||
* 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 {
|
||||
GaussianFactorGraph::shared_ptr graph(new GaussianFactorGraph());
|
||||
BOOST_FOREACH(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)));
|
||||
}
|
||||
}
|
||||
return graph;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
LPState iterate(const LPState& state) const {
|
||||
static bool debug = false;
|
||||
|
||||
// Solve with the current working set
|
||||
// LP: project the objective neggradient to the constraint's null space
|
||||
// to find the direction to move
|
||||
VectorValues newValues = solveWithCurrentWorkingSet(state.values,
|
||||
state.workingSet);
|
||||
// if (debug) state.workingSet.print("Working set:");
|
||||
if (debug) (newValues - state.values).print("New direction:");
|
||||
|
||||
// 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
|
||||
// Compute lambda from the dual graph
|
||||
// LP: project the objective's gradient onto each constraint gradient to obtain the dual scaling factors
|
||||
// is it true??
|
||||
if (debug) cout << "Building dual graph..." << endl;
|
||||
GaussianFactorGraph::shared_ptr dualGraph = buildDualGraph(
|
||||
state.workingSet, newValues);
|
||||
if (debug) dualGraph->print("Dual graph: ");
|
||||
VectorValues duals = dualGraph->optimize();
|
||||
if (debug) duals.print("Duals :");
|
||||
|
||||
// LP: see which ineq constraint has wrong pulling direction, i.e., dual < 0
|
||||
int leavingFactor = identifyLeavingConstraint(state.workingSet, duals);
|
||||
if (debug) cout << "leavingFactor: " << leavingFactor << endl;
|
||||
|
||||
// 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!
|
||||
// ...
|
||||
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);
|
||||
}
|
||||
}
|
||||
else {
|
||||
// If we CAN make some progress, i.e. p_k != 0
|
||||
// Adapt stepsize if some inactive constraints complain about this move
|
||||
// LP: projection on nullspace is NOT zero:
|
||||
// find and put a blocking inactive constraint to the working set,
|
||||
// otherwise the problem is unbounded!!!
|
||||
double alpha;
|
||||
int factorIx;
|
||||
VectorValues p = newValues - state.values;
|
||||
boost::tie(alpha, factorIx) = // using 16.41
|
||||
computeStepSize(state.workingSet, state.values, p);
|
||||
if (debug) cout << "alpha, factorIx: " << alpha << " " << factorIx << " "
|
||||
<< endl;
|
||||
|
||||
// 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;
|
||||
if (debug) newValues.print("New solution:");
|
||||
|
||||
return LPState(newValues, state.duals, newWorkingSet, false,
|
||||
state.iterations + 1);
|
||||
}
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
/**
|
||||
* 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,
|
||||
* i.e. -g is the direction we wish to follow to decrease the cost.
|
||||
*
|
||||
* Essentially, we try to match the direction d = x-xk with -g as much as possible
|
||||
* subject to the condition that x needs to be on the constraint surface, i.e., d is
|
||||
* along the surface's subspace.
|
||||
*
|
||||
* The least-square solution of this quadratic subject to a set of linear constraints
|
||||
* is the projection of the gradient onto the constraints' subspace
|
||||
*/
|
||||
GaussianFactorGraph::shared_ptr createLeastSquareFactors(
|
||||
const LinearCost& cost, const VectorValues& xk) const {
|
||||
GaussianFactorGraph::shared_ptr graph(new GaussianFactorGraph());
|
||||
KeyVector keys = cost.keys();
|
||||
|
||||
for (LinearCost::const_iterator it = cost.begin(); it != cost.end(); ++it) {
|
||||
size_t dim = cost.getDim(it);
|
||||
Vector b = xk.at(*it) - cost.getA(it).transpose(); // b = xk-g
|
||||
graph->push_back(JacobianFactor(*it, eye(dim), b));
|
||||
}
|
||||
|
||||
return graph;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
VectorValues solveWithCurrentWorkingSet(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) {
|
||||
if (factor->active()) workingGraph.push_back(factor);
|
||||
}
|
||||
return workingGraph.optimize();
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
/// 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));
|
||||
}
|
||||
}
|
||||
return Aterms;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
JacobianFactor::shared_ptr 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
|
||||
TermsContainer Aterms = collectDualJacobians<LinearEquality>(key,
|
||||
lp_.equalities, equalityVariableIndex_);
|
||||
TermsContainer AtermsInequalities = collectDualJacobians<LinearInequality>(
|
||||
key, workingSet, inequalityVariableIndex_);
|
||||
Aterms.insert(Aterms.end(), AtermsInequalities.begin(),
|
||||
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
|
||||
}
|
||||
else {
|
||||
return boost::make_shared<JacobianFactor>();
|
||||
}
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
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;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
int identifyLeavingConstraint(const InequalityFactorGraph& workingSet,
|
||||
const VectorValues& duals) 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 max_s = 0.0;
|
||||
for (size_t factorIx = 0; factorIx < workingSet.size(); ++factorIx) {
|
||||
const LinearInequality::shared_ptr& factor = workingSet.at(factorIx);
|
||||
if (factor->active()) {
|
||||
double s = duals.at(factor->dualKey())[0];
|
||||
if (s > max_s) {
|
||||
worstFactorIx = factorIx;
|
||||
max_s = s;
|
||||
}
|
||||
}
|
||||
}
|
||||
return worstFactorIx;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
std::pair<double, int> computeStepSize(
|
||||
const InequalityFactorGraph& workingSet, const VectorValues& xk,
|
||||
const VectorValues& p) const {
|
||||
static bool debug = false;
|
||||
|
||||
double minAlpha = std::numeric_limits<double>::infinity();
|
||||
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;
|
||||
if (debug) cout << "alpha: " << alpha << endl;
|
||||
|
||||
// We want the minimum of all those max alphas
|
||||
if (alpha < minAlpha) {
|
||||
closestFactorIx = factorIx;
|
||||
minAlpha = alpha;
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
return std::make_pair(minAlpha, closestFactorIx);
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
InequalityFactorGraph identifyActiveConstraints(
|
||||
const InequalityFactorGraph& inequalities,
|
||||
const VectorValues& initialValues, const VectorValues& duals) const {
|
||||
InequalityFactorGraph workingSet;
|
||||
BOOST_FOREACH(const LinearInequality::shared_ptr& factor, inequalities) {
|
||||
LinearInequality::shared_ptr workingFactor(new LinearInequality(*factor));
|
||||
|
||||
double error = workingFactor->error(initialValues);
|
||||
// TODO: find a feasible initial point for LPSolver.
|
||||
// For now, we just throw an exception
|
||||
if (error > 0) throw InfeasibleInitialValues();
|
||||
|
||||
if (fabs(error) < 1e-7) {
|
||||
workingFactor->activate();
|
||||
}
|
||||
else {
|
||||
workingFactor->inactivate();
|
||||
}
|
||||
workingSet.push_back(workingFactor);
|
||||
}
|
||||
return workingSet;
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
/** Optimize with the provided feasible initial values
|
||||
* TODO: throw exception if the initial values is not feasible wrt inequality constraints
|
||||
*/
|
||||
pair<VectorValues, VectorValues> optimize(const VectorValues& initialValues,
|
||||
const VectorValues& duals = VectorValues()) const {
|
||||
|
||||
// Initialize workingSet from the feasible initialValues
|
||||
InequalityFactorGraph workingSet = identifyActiveConstraints(
|
||||
lp_.inequalities, initialValues, duals);
|
||||
LPState state(initialValues, duals, workingSet, false, 0);
|
||||
|
||||
/// main loop of the solver
|
||||
while (!state.converged) {
|
||||
state = iterate(state);
|
||||
}
|
||||
|
||||
return make_pair(state.values, state.duals);
|
||||
}
|
||||
|
||||
//******************************************************************************
|
||||
/**
|
||||
* Optimize without initial values
|
||||
* TODO: Find a feasible initial solution wrt inequality constraints
|
||||
*/
|
||||
// pair<VectorValues, VectorValues> optimize() const {
|
||||
//
|
||||
// // Initialize workingSet from the feasible initialValues
|
||||
// InequalityFactorGraph workingSet = identifyActiveConstraints(
|
||||
// lp_.inequalities, initialValues, duals);
|
||||
// LPState state(initialValues, duals, workingSet, false, 0);
|
||||
//
|
||||
// /// main loop of the solver
|
||||
// while (!state.converged) {
|
||||
// state = iterate(state);
|
||||
// }
|
||||
//
|
||||
// return make_pair(state.values, state.duals);
|
||||
// }
|
||||
|
||||
};
|
||||
|
||||
/**
|
||||
* Abstract class to solve for an initial value of an LP problem
|
||||
*/
|
||||
class LPInitSolver {
|
||||
protected:
|
||||
const LP& lp_;
|
||||
const LPSolver& lpSolver_;
|
||||
|
||||
public:
|
||||
LPInitSolver(const LPSolver& lpSolver) :
|
||||
lp_(lpSolver.lp()), lpSolver_(lpSolver) {
|
||||
}
|
||||
virtual ~LPInitSolver() {};
|
||||
virtual VectorValues solve() const = 0;
|
||||
};
|
||||
|
||||
/**
|
||||
* This LPInitSolver implements the strategy in Matlab:
|
||||
* http://www.mathworks.com/help/optim/ug/linear-programming-algorithms.html#brozyzb-9
|
||||
|
|
|
|||
Loading…
Reference in New Issue