Dual AMA iterative solver (Alternating Minimization Algorithm on dual formuation of quadratic optimization problem). More...

#include <ADMM.hpp>

Inheritance diagram for bogus::DualAMA< BlockMatrixType >:

Public Types
typedef ConstrainedSolverBase < DualAMA, BlockMatrixType >	Base

typedef Base::GlobalProblemTraits	GlobalProblemTraits

typedef GlobalProblemTraits::Scalar	Scalar

typedef LocalProblemTraits < Base::BlockTraits::RowsPerBlock, Scalar >	BlockProblemTraits

typedef BlockMatrixTraits < BlockMatrixType >	BlockTraits

typedef Signal< unsigned, Scalar >	CallBackType

Public Member Functions
	DualAMA ()
	Default constructor – you will have to call setMatrix() before using the solve() function.

	DualAMA (const BlockObjectBase< BlockMatrixType > &matrix)
	Constructor with the system matrix.

template<typename NSLaw , typename MatrixT , typename RhsT , typename ResT >
Scalar	solve (const NSLaw &law, const BlockObjectBase< MatrixT > &A, const RhsT &f, const RhsT &w, ResT &v, ResT &r) const
	Solve function using default variant.

template<admm::Variant variant, typename NSLaw , typename MatrixT , typename RhsT , typename ResT >
Scalar	solve (const NSLaw &law, const BlockObjectBase< MatrixT > &A, const RhsT &f, const RhsT &w, ResT &v, ResT &r) const
	Solve function with variant as template argument.

template<admm::Variant variant, typename NSLaw , typename AType , typename BType , typename HType , typename PrecondT , typename RhsT , typename ORhsT , typename ResT , typename OResT >
Scalar	solveWithLinearConstraints (const NSLaw &law, const BlockObjectBase< AType > &A, const BlockObjectBase< BType > &B, const BlockObjectBase< HType > &H, const PrecondT &preconditioner, const RhsT &f, const ORhsT &k, const RhsT &w, ResT &v, OResT &p, ResT &r, Scalar stepRatio=1) const
	Idem with constraint ( B v + k = 0 )

DualAMA &	setMatrix (const BlockObjectBase< BlockMatrixType > &matrix)
	Sets the problem matrix – the one defining the constraints.

void	setFpStepSize (const Scalar size)
	Sets the step size for updating the dual variable (forces).

void	setProjStepSize (const Scalar size)

void	setDefaultVariant (admm::Variant variant)
	Sets the variant that will be used when calling solve() without template arguments.

Scalar	fpStepSize () const

Scalar	projStepSize () const

void	setLineSearchIterations (const unsigned lsIterations)
	Sets the maximum number of line-search iterations.

void	setLineSearchOptimisticFactor (const Scalar lsOptimisticFactor)

void	setLineSearchPessimisticFactor (const Scalar lsPessimisticFactor)

unsigned	lineSearchIterations () const

Scalar	lineSearchOptimisticFactor () const

Scalar	lineSearchPessimisticFactor () const

void	useInfinityNorm (bool useInfNorm)
	Sets whether the solver will use the infinity norm instead of the l1 one to compute the global residual from the local ones.

bool	usesInfinityNorm () const

Scalar	eval (const NSLaw &law, const ResT &y, const RhsT &x) const
	Eval the current global residual as a function of the local ones. More...

void	projectOnConstraints (const NSLaw &projector, VectorT &x) const
	Projects the variable `x` on the constraints defined by `projector`.

void	dualityCOV (const NSLaw &law, const RhsT &b, ResT &x) const
	Compute associated change of variable (see NSLaw)

Scalar	solve (const NSLaw &law, const RhsT &b, ResT &x) const

void	setMaxIters (unsigned maxIters)
	For iterative solvers: sets the maximum number of iterations.

unsigned	maxIters () const

void	setTol (Scalar tol)
	For iterative solvers: sets the solver tolerance.

Scalar	tol () const

CallBackType &	callback ()
	Callback hook; will be triggered every N iterations, depending on the solver. More...

const CallBackType &	callback () const

const BlockObjectBase < BlockMatrixType > &	matrix () const

Protected Types
typedef Base::Index	Index

Protected Member Functions
void	init ()
	Sets up the default values for all parameters.

void	updateScalings ()

Protected Attributes
Scalar	m_fpStepSize

Scalar	m_projStepSize

admm::Variant	m_defaultVariant

unsigned	m_lsIters

Scalar	m_lsOptimisticFactor

Scalar	m_lsPessimisticFactor

GlobalProblemTraits::DynVector	m_scaling

bool	m_useInfinityNorm
	See useInfinityNorm(). Defaults to false.

const BlockObjectBase < BlockMatrixType > *	m_matrix
	Pointer to the matrix of the system.

unsigned	m_maxIters
	See setMaxIters()

Scalar	m_tol
	See setTol()

CallBackType	m_callback

Detailed Description

template<typename BlockMatrixType>
class bogus::DualAMA< BlockMatrixType >

Dual AMA iterative solver (Alternating Minimization Algorithm on dual formuation of quadratic optimization problem).

Minimizes .5 r' M A^-1 M' r + r' ( w - M A^-1 f ) for r in C

as min H(x) + G(r)  , x = M' r
with H(x) = .5 x' A^-1 x - x' A^-1 f
     G(r) = I_C(r) + r'w

thanks to the identities
 prox_{l,G} (y) = prox_{l,Ic}( y - lw ) = Pi_C ( y - lw )
and
 inf_x  H(x) - < v, x > = A v + f

Main advantage of this solver is that it does not require inverting or solving linear system with the stiffness matrix A.

Warning: Experimental

Member Function Documentation

template<typename BlockMatrixType >

CallBackType& bogus::BlockSolverBase< BlockMatrixType >::callback ( )

inherited

Callback hook; will be triggered every N iterations, depending on the solver.

Useful to monitor the convergence of the solver. Can be connected to a function that takes an unsigned and a Scalar as parameters. The first argument will be the current iteration number, and the second the current residual.

See Also: Signal< unsigned, Scalar >

Scalar bogus::ConstrainedSolverBase< DualAMA< BlockMatrixType > , BlockMatrixType >::eval	(	const NSLaw &	law,
		const ResT &	y,
		const RhsT &	x
	)		const

inherited

Eval the current global residual as a function of the local ones.

y should be such that y = m_matrix * x + rhs

Returns

the current residual err defined as follow :

if m_useInfinityNorm is true, then err $:= \max\limits_{1 \leq i \leq n } law.eval(i,x_i,y_i)$
else err := $\frac 1 {n+1} \sum\limits_{1 \leq i \leq n } law.eval(i,x_i,y_i)$

template<typename BlockMatrixType >

void bogus::DualAMA< BlockMatrixType >::setLineSearchOptimisticFactor ( const Scalar lsOptimisticFactor )

Sets the amount by which the step size will be multiplied at the beginninf of each PG iteration. Should be greater than 1

template<typename BlockMatrixType >

void bogus::DualAMA< BlockMatrixType >::setLineSearchPessimisticFactor ( const Scalar lsPessimisticFactor )

Sets the amount by which the step size will be multiplied at the end of each line-search iterations. Should be in ]0,1[

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

ADMM.hpp

Public Types

Public Member Functions

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

template<typename BlockMatrixType> class bogus::DualAMA< BlockMatrixType >

Member Function Documentation

template<typename BlockMatrixType>
class bogus::DualAMA< BlockMatrixType >