Definition of the class PrimalDual. More...

#include <PrimalDual.h>

Inheritance diagram for PrimalDual:

Public Member Functions
	PrimalDual (SubGrad slvr, istream iStrm=0)
	Constructor of the class, which derives from both Deflection and Stepsize. More...

Other initializations
void	SetVOLLog (ostream *outs=0, const char lvl=0)

void	Format (void)

Reading the solution
void	NewDEF (void)
	The variant requires thats DR must be computed before SR. More...

void	NewStep (void)

cHpNum	GetDFLCoeff (void)

HpNum	GetStepsize (bool StepIsIncr=false)

HpNum	GetLev (void)

HpNum	GetBeta (void)

void	SetMaxBeta (const HpNum alpha)

Public Member Functions inherited from Deflection
	Deflection (SubGrad *slvr)
	Constructor of the class. More...

virtual const bool	DoSS (void)
	Returns true if a Serious Step (SS) takes place. More...

virtual cHpNum	Delta (void)
	Returns the expected improvement in the objective function [see DoSS()]. More...

virtual	~Deflection ()

Public Member Functions inherited from Stepsize
	Stepsize (SubGrad slvr, istream iStrm=0)
	Constructor of the class. More...

	Stepsize (SubGrad slvr, istream iStrm=0)
	Constructor of the class. More...

virtual void	SetSTPLog (ostream *outs=0, const char lvl=0)
	The class outputs "log" information onto the ostream pointed by outs. More...

virtual void	SetSTPLog (ostream *outs=0, const char lvl=0)
	The class outputs "log" information onto the ostream pointed by outs. More...

virtual bool	NeedsdkM1Gk (void)
	Returns true if the stepsize requires the scalar product $d_{i-1}^{\top} g_i$ . More...

virtual bool	NeedsdkM1Gk (void)
	Returns true if the stepsize requires the scalar product $d_{i-1}^{\top} g_i$ . More...

virtual	~Stepsize ()

virtual	~Stepsize ()

Additional Inherited Members
Protected Member Functions inherited from Deflection
FiOracle *	GetOracle (void)
	Returns the pointer to FiOracle. More...

HpNum	GetStepsize (void)
	Returns the stepsize $\nu_i$ . More...

cHpNum	GetGiNorm (void)
	Returns the norm of the subgradient . More...

cHpNum	GetDNorm (void)
	Returns the norm of the direction . More...

cHpNum	GetdGk (void)
	Returns the scalar product $g_i^{\top} d_i$ . More...

cHpNum	GetSigma (void)
	Returns the linearization error $\sigma_i$ . More...

cHpNum	GetEpsilon (void)
	Returns the linearization error $\epsilon_i$ . More...

cHpNum	ReadFVal (void)
	Returns the full function $f(\lambda_i)$ . More...

Protected Member Functions inherited from Stepsize
virtual bool	UpdateTargetLevel (void)
	It tries to provide a new target level $f^{lev}_i$ . More...

virtual bool	UpdateTargetLevel (void)
	It tries to provide a new target level $f^{lev}_i$ . More...

HpNum	GetCoeffDefl (void)
	Returns the deflection coefficient $\alpha_i$ . More...

FiOracle *	GetOracle (void)
	Returns the pointer to FiOracle. More...

cHpNum	GetGiNorm (void)
	Returns the norm of the subgradient . More...

cHpNum	GetDNorm (void)
	Returns the norm of the direction . More...

cHpNum	GetdGk (void)
	Returns the scalar product $g_i^{\top} d_i$ . More...

HpNum	GetdkM1Gk (void)
	Returns the scalar product $g_i^{\top} d_{i-1}$ . More...

Index	GetNItIcr (void)
	Returns NItIncr, the parameter for incremental iterations [see SubGrad.h].

cHpNum	ReadFkVal (void)
	Returns FiLambda [ see SubGrad.h ]. More...

cHpNum	ReadFiBar (void)
	Returns FiBar [ see SubGrad.h ]. More...

HpNum	GetCoeffDefl (void)
	Returns the deflection coefficient $\alpha_i$ . More...

FiOracle *	GetOracle (void)
	Returns the pointer to FiOracle. More...

cHpNum	GetGiNorm (void)
	Returns the norm of the subgradient . More...

cHpNum	GetDNorm (void)
	Returns the norm of the direction . More...

cHpNum	GetdGk (void)
	Returns the scalar product $g_i^{\top} d_i$ . More...

HpNum	GetdkM1Gk (void)
	Returns the scalar product $g_i^{\top} d_{i-1}$ . More...

Index	GetNItIcr (void)
	Returns NItIncr, the parameter for incremental iterations [see SubGrad.h].

cHpNum	ReadFkVal (void)
	Returns FiLambda [ see SubGrad.h ]. More...

cHpNum	ReadFiBar (void)
	Returns FiBar [ see SubGrad.h ]. More...

Protected Attributes inherited from Deflection
SubGrad *	Solver
	(pointer to) the SubGrad solver

ostream *	VOLLog
	the output stream object

char	VOLLLvl
	the "level of verbosity"

Protected Attributes inherited from Stepsize
SubGrad *	Solver
	(pointer to) the SubGrad solver

ostream *	STPLog
	the output stream object

char	STPLLvl
	the "level of verbosity"

HpNum	FiLev
	the target level $f^{lev}_i$

HpNum	Beta
	beta factor $\beta_i$

HpNum	MaxBeta
	maximum value for beta factor

HpNum	LpsFct
	scaling factor

Detailed Description

Definition of the class PrimalDual.

This class implements two variants of the Primal-Dual subgradient method (PDSM): simple and weighted averages, under a unified SM scheme. The method has a fixed stability center, and the direction $ d_i $ can be regarded as the average of all the previous weighted subgradients, i.e.:

$d_i = ( \sum_{k=1}^i \upsilon_k g_k) / \Delta_i \quad,\quad \Delta_i = \sum_{k=1}^i \upsilon_k$

It is worth mentioning that the subgradient weights $\upsilon_k$ can be non-vanishing as $k\rightarrow \infty$ . The stepsize rule (SR) and the deflection rule (DR), respectively, are:

$\alpha_i = \upsilon_i / \Delta_i \quad,\quad \nu_i = \Delta_i / \omega_i$

where $\omega_i$ is chosen in a suitable way.

Constructor & Destructor Documentation

PrimalDual	(	SubGrad *	slvr,
		istream *	iStrm = `0`
	)

inline

Constructor of the class, which derives from both Deflection and Stepsize.

Since the constructor of PrimalDual is executed after the one of Stepsize, the following parameters specific for PrimalDual have to be found in the stream after those of the base class Stepsize [see the comments to the constructor of Stepsize]:

bool average [true] if true simple averages are used, otherwise weighted averages are used

For this class, the general parameter LpsFct -defined in Stepsize.h- represents the gamma factor F used to set $\omega_i$ .

References Deflection::Format(), FiOracle::GetGlobalLipschitz(), Deflection::GetOracle(), Deflection::GetStepsize(), Stepsize::LpsFct, Deflection::SetVOLLog(), Deflection::VOLLLvl, and Deflection::VOLLog.

Member Function Documentation

void NewDEF ( void )

inlinevirtual

The variant requires thats DR must be computed before SR.

Hence, the call to NewDEF comes before the one to NewStep.

Implements Deflection.

References Deflection::GetGiNorm(), Stepsize::LpsFct, and Deflection::Solver.

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation