94 lines
3.2 KiB
C++
94 lines
3.2 KiB
C++
/**
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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 Duy Nguyen Ta
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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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#include <gtsam_unstable/linear/LPState.h>
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#include <gtsam_unstable/linear/LP.h>
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#include <gtsam_unstable/linear/ActiveSetSolver.h>
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#include <gtsam_unstable/linear/LinearCost.h>
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#include <gtsam/linear/VectorValues.h>
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#include <boost/range/adaptor/map.hpp>
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namespace gtsam {
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class LPSolver: public ActiveSetSolver {
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const LP &lp_; //!< the linear programming problem
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public:
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/// Constructor
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LPSolver(const LP &lp);
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const LP &lp() const {
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return lp_;
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}
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/*
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* This function performs an iteration of the Active Set Method for solving
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* LP problems. At the end of this iteration the problem should either be found
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* to be unfeasible, solved or the current state changed to reflect a new
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* working set.
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*/
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LPState iterate(const LPState &state) const;
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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 buildCostFunction(const VectorValues &xk) const;
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GaussianFactorGraph buildWorkingGraph(
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const InequalityFactorGraph& workingSet, const VectorValues& xk) const;
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/*
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* A dual factor takes the objective function and a set of constraints.
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* It then creates a least-square approximation of the lagrangian multipliers
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* for the following problem: f' = - lambda * g' where f is the objection
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* function g are dual factors and lambda is the lagrangian multiplier.
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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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/// TODO(comment)
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boost::tuple<double, int> computeStepSize(
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const InequalityFactorGraph &workingSet, const VectorValues &xk,
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const VectorValues &p) const;
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/*
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* Given an initial value this function determine which constraints are active
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* which can be used to initialize the working set.
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* A constraint Ax <= b is active if we have an x' s.t. Ax' = b
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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,
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bool useWarmStart = false) const;
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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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* TODO: comment duals
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*/
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pair<VectorValues, VectorValues> optimize(const VectorValues &initialValues,
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const VectorValues &duals = VectorValues(), bool useWarmStart = false) const;
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/**
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* Optimize without initial values.
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*/
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pair<VectorValues, VectorValues> optimize() const;
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};
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} // namespace gtsam
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