gtsam::LPInitSolver Class Reference

#include <LPInitSolver.h>

Public Member Functions
	LPInitSolver (const LP &lp)
	Construct with an LP problem. More...
VectorValues	solve () const

Private Member Functions
InequalityFactorGraph	addSlackVariableToInequalities (Key yKey, const InequalityFactorGraph &inequalities) const
	Turn Cx <= d into Cx - y <= d factors. More...
LP::shared_ptr	buildInitialLP (Key yKey) const
	build initial LP More...
GaussianFactorGraph::shared_ptr	buildInitOfInitGraph () const
std::vector< std::pair< Key, Matrix > >	collectTerms (const LinearInequality &factor) const
	Collect all terms of a factor into a container. More...
double	compute_y0 (const VectorValues &x0) const
	y = max_j ( Cj*x0 - dj ) – due to the inequality constraints y >= Cx - d More...

Private Attributes
const LP &	lp_

Friends
class	LPInitSolverInitializationTest

Detailed Description

This LPInitSolver implements the strategy in Matlab: http://www.mathworks.com/help/optim/ug/linear-programming-algorithms.html#brozyzb-9 Solve for x and y: min y st Ax = b Cx - y <= d where , , and Ax = b and Cx <= d is the constraints of the original problem.

If the solution for this problem {x*,y*} has y* <= 0, we'll have x* a feasible initial point of the original problem otherwise, if y* > 0 or the problem has no solution, the original problem is infeasible.

The initial value of this initial problem can be found by solving min ||x||^2 s.t. Ax = b to have a solution x0 then y = max_j ( Cj*x0 - dj ) – due to the constraints y >= Cx - d

WARNING: If some xj in the inequality constraints does not exist in the equality constraints, set them as zero for now. If that is the case, the original problem doesn't have a unique solution (it could be either infeasible or unbounded). So, if the initialization fails because we enforce xj=0 in the problematic inequality constraint, we can't conclude that the problem is infeasible. However, whether it is infeasible or unbounded, we don't have a unique solution anyway.

Definition at line 52 of file LPInitSolver.h.

Constructor & Destructor Documentation

LPInitSolver()

gtsam::LPInitSolver::LPInitSolver ( const LP &  lp )

inline

Construct with an LP problem.

Definition at line 58 of file LPInitSolver.h.

Member Function Documentation

addSlackVariableToInequalities()

InequalityFactorGraph gtsam::LPInitSolver::addSlackVariableToInequalities ( Key  yKey, const InequalityFactorGraph &  inequalities  ) const

private

Turn Cx <= d into Cx - y <= d factors.

Definition at line 98 of file LPInitSolver.cpp.

buildInitialLP()

LP::shared_ptr gtsam::LPInitSolver::buildInitialLP ( Key  yKey ) const

private

build initial LP

Definition at line 51 of file LPInitSolver.cpp.

buildInitOfInitGraph()

GaussianFactorGraph::shared_ptr gtsam::LPInitSolver::buildInitOfInitGraph ( ) const

private

Build the following graph to solve for an initial value of the initial problem min ||x||^2 s.t. Ax = b

Definition at line 62 of file LPInitSolver.cpp.

collectTerms()

std::vector< std::pair< Key, Matrix > > gtsam::LPInitSolver::collectTerms ( const LinearInequality &  factor ) const

private

Collect all terms of a factor into a container.

Definition at line 88 of file LPInitSolver.cpp.

compute_y0()

double gtsam::LPInitSolver::compute_y0 ( const VectorValues &  x0 ) const

private

y = max_j ( Cj*x0 - dj ) – due to the inequality constraints y >= Cx - d

Definition at line 78 of file LPInitSolver.cpp.

solve()

VectorValues gtsam::LPInitSolver::solve

(

)

const

Returns

a feasible initialization point

Definition at line 27 of file LPInitSolver.cpp.

Friends And Related Function Documentation

LPInitSolverInitializationTest

friend class LPInitSolverInitializationTest

friend

Definition at line 85 of file LPInitSolver.h.

Member Data Documentation

lp_

const LP& gtsam::LPInitSolver::lp_

private

Definition at line 54 of file LPInitSolver.h.

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The documentation for this class was generated from the following files:

• LPInitSolver.h
• LPInitSolver.cpp