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ConstrLpBallSolver Class Reference

LinearConstrSolver for FrankWolfe algorithm. More...

## Public Member Functions

ConstrLpBallSolver (const double p)
Construct the solver of constrained problem. More...

ConstrLpBallSolver (const double p, const arma::vec lambda)
Construct the solver of constrained problem, with regularization parameter lambda here. More...

arma::vec Lambda () const
Get the regularization parameter. More...

arma::vec & Lambda ()
Modify the regularization parameter. More...

void Optimize (const arma::mat &v, arma::mat &s)
Optimizer of Linear Constrained Problem for FrankWolfe. More...

double P () const
Get the p-norm. More...

double & P ()
Modify the p-norm. More...

bool RegFlag () const
Get regularization flag. More...

bool & RegFlag ()
Modify regularization flag. More...

## Detailed Description

LinearConstrSolver for FrankWolfe algorithm.

Constraint domain given in the form of lp ball. That is, given , solve when is a regularized lp ball. That is,

If is not given in the constructor, default is using all for all .

In applications such as Orthogonal Matching Pursuit (OMP), could be ideally set to the norm of the elements in the dictionary.

For : take (one) , then the solution is:

For : the solution is

For : the solution is

Definition at line 55 of file constr_lpball.hpp.

## ◆ ConstrLpBallSolver() [1/2]

 ConstrLpBallSolver ( const double p )
inline

Construct the solver of constrained problem.

The constrained domain should be unit lp ball for this class.

Parameters
 p The constraint is unit lp ball.

Definition at line 64 of file constr_lpball.hpp.

## ◆ ConstrLpBallSolver() [2/2]

 ConstrLpBallSolver ( const double p, const arma::vec lambda )
inline

Construct the solver of constrained problem, with regularization parameter lambda here.

Parameters
 p The constraint is unit lp ball. lambda Regularization parameter.

Definition at line 74 of file constr_lpball.hpp.

## ◆ Lambda() [1/2]

 arma::vec Lambda ( ) const
inline

Get the regularization parameter.

Definition at line 145 of file constr_lpball.hpp.

## ◆ Lambda() [2/2]

 arma::vec& Lambda ( )
inline

Modify the regularization parameter.

Definition at line 147 of file constr_lpball.hpp.

## ◆ Optimize()

 void Optimize ( const arma::mat & v, arma::mat & s )
inline

Optimizer of Linear Constrained Problem for FrankWolfe.

Parameters
 v Input local gradient. s Output optimal solution in the constrained domain (lp ball).

Definition at line 85 of file constr_lpball.hpp.

References Log::Fatal, and mlpack::math::Sign().

## ◆ P() [1/2]

 double P ( ) const
inline

Get the p-norm.

Definition at line 135 of file constr_lpball.hpp.

## ◆ P() [2/2]

 double& P ( )
inline

Modify the p-norm.

Definition at line 137 of file constr_lpball.hpp.

## ◆ RegFlag() [1/2]

 bool RegFlag ( ) const
inline

Get regularization flag.

Definition at line 140 of file constr_lpball.hpp.

## ◆ RegFlag() [2/2]

 bool& RegFlag ( )
inline

Modify regularization flag.

Definition at line 142 of file constr_lpball.hpp.

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