ADMM (Alternating Direction Method of Multipliers ) iterative solver. More...

#include <ADMM.hpp>

Inheritance diagram for bogus::ADMM< BlockMatrixType >:

Public Types
typedef ConstrainedSolverBase < ADMM, 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
	ADMM ()
	Default constructor – you will have to call setMatrix() before using the solve() function.

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

template<admm::Variant variant, typename NSLaw , typename ProxOp , typename RhsT , typename ResT >
Scalar	solve (const NSLaw &law, const ProxOp &op, const RhsT &w, ResT &v, ResT &r) const

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

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

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

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

Scalar	stepSize () 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_stepSize

admm::Variant	m_defaultVariant

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::ADMM< BlockMatrixType >

ADMM (Alternating Direction Method of Multipliers ) iterative solver.

Minimizes J(v) with ( M v + w ) in C, C defined by the NSLaw in the solve() function.

Requires ability to evaluate $prox_{\lambda} J( x ) := \min_y J(y) + \frac 1 {2 \lambda} \Vert x - y \Vert^2$

See Also: QuadraticProxOp

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< ADMM< 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 >

template<admm::Variant variant, typename NSLaw , typename ProxOp , typename RhsT , typename ResT >

Scalar bogus::ADMM< BlockMatrixType >::solve	(	const NSLaw &	law,
		const ProxOp &	op,
		const RhsT &	w,
		ResT &	v,
		ResT &	r
	)		const

Find the minimizer of J(v), ( Mv + w in C ) with J(v) defined through its proximal operator, op and C defined by law

Parameters

law	should define projectOnConstraints()
op	should define a `eval(Rhs& rhs, Res& res)` function computing `res` as $prox_{J, 1/\lambda}( rhs/\lambda )$ and `coefficient()` returning $\lambda$

See Also: QuadraticProxOp

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::ADMM< BlockMatrixType >

Member Function Documentation

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