QqpDualFunc Class Reference

A base class for evaluating the dual function. More...

#include <dualqqp.h>

Inheritance diagram for QqpDualFunc:

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Collaboration diagram for QqpDualFunc:

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List of all members.

Public Member Functions
	QqpDualFunc (MinlpProblem &qqp_, Param &param_, Pointer< ostream > out_func_p_=out_out_p, Pointer< ostream > out_func_log_p_=out_log_p)
	Constructor for a MinlpReform and a shift.
virtual int	valgrad (double &val, UserVector< double > &g, const UserVector< double > &z) const
	Evaluates the function value and computes the subgradient of the dual function.
double	eval (const UserVector< double > &z) const
	Evaluates this function for a dvector.
void	grad (UserVector< double > &g, const UserVector< double > &x) const
	Computes the gradient of this function.
virtual void	HessMult (UserVector< double > &y, const UserVector< double > &x, const UserVector< double > &z) const
	Does nothing.
dvector	get_dual_point () const
	Set the Lagrange multipliers of the quadratic box constraints.
dvector	get_dual_point (dvector &ext_dual_point) const
	The dual point of the original qqp for an extended dual point.
double	get_dual_val () const
	The last dual value.
double	get_dual_val (dvector &ext_dual_point) const
	The dual value for an extended dual point.
dvector	get_orig_point (int use_eig_vec=0) const
	Gives the solution point of the Lagrangian function.
dvector	get_orig_point (dvector &ext_dual_point, int use_eig_vec=0) const
	The dual value for an extended dual point.
int	nr_of_orig_points () const
	The number of eigenvectors, which are computed in each evaluation.
void	print (ostream &out) const
	Print's a lot of information about this function.
Public Attributes
int	num_matmult
	number of matrix vector multiplications
double	eig_time
	time spent by the eigenvalue calculation
dvector	dual_point
	The dual variables of the extended (!) dual function.
Protected Types
enum	b_type { LIN, QUAD, EXTQUAD }
	The different block-types. More...
Protected Member Functions
int	num_qbox () const
	The number of quadratic-box-constraints.
int	num_blocks () const
	The number of blocks.
void	init_ext ()
	Check's, if partial Lagrange problem is extended Set ext[k] to true, if the bounds are not symmetric or no linear part exists.
void	init ()
	Initialization of the dual function.
void	set_ball_con ()
	Initialize the ball constraints.
void	get_bc (double &c_, dvector &b_, SepQcFunc &q)
	Compute's modified b,c values for a SepQcFunc.
void	set_bc ()
	Initialize the modified b,c-values.
int	set_dual_val () const
	Compute the value of the dual function.
double	eval_mod_con (int con_nr) const
	Evaluates a modified constraint.
double	eval_mod_obj () const
	Evaluates the modified objective.
void	set_subgrad () const
	Compute a subgradient of the dual function.
Protected Attributes
vector< b_type >	block_type
	Indicates for each block, which type the block of the lagrange problem has.
ivector	i_ext
	The indices of the new quadratic box constraints.
int	num_ext
	The number of extended blocks.
ivector	i_q
	The index of the start of the quadratric box constraints for the k-th block.
int	n_q
	The number of quadratic variables.
dvector	mid_point
	The mid point of the box = 0.5*(lower+upper).
BlockMatrix	W
	The half-length of the edges of the box.
dvector	radius
	The radius of the ball-constraints.
vector< bool >	ball_con
	The type of the ball-constraints.
vector< dvector >	b_con
	The type of scaling (currently not used).
dvector	b_obj
	The modified b-value for the objective-function.
dvector	c_con
	The modified c-values for the constraints.
double	c_obj
	The modified c-value for the objective-function.
vector< Pointer< UserMatrix > >	A_lag
	The block matrices of the modified Lagrangian Set in init.
vector< dvector >	b_lag
	The linear part of the modified Lagrangian Set in init.
double	c_lag
	The constant part of the modified Lagrangian Set in init.
dvector	x_lag
	The Lagrange solution.
double	dual_val
	current value of the dual function.
dvector	subgrad
	The subgradient.
vector< vector< double > >	eig_val
	minimal eigenvalues of A_lag[k], k=0,.
vector< vector< dvector > >	eig_vec
	eigenvectors of A_lag[k], k=0,.
Friends
class	QqpMatrix
class	QqpExtMatrix

Detailed Description

A base class for evaluating the dual function.

$D(\lambda )= \sum_{k=1}^{l-1}(\rho_k^2\cdot \min\{eig_{min}(\tilde A_k(\lambda)),0\} +\sum_{j=r_l}^{r_{l+1}}\min\{\underline x_{j}b_{j}(\lambda ), \bar x_{j}b_{j}(\lambda )\})+\tilde c(\lambda )$

assignment of the dual variables:

0:n-1 quadratic box-constraints of original variables

n:n+block_size-1 quadratic box-constraints of the new variables

block_size+n:block_size+n+con_size-1 remaining constraints

Definition at line 100 of file dualqqp.h.

Member Enumeration Documentation

enum QqpDualFunc::b_type [protected]

The different block-types.

QUAD: the hessian of this block is non-zero and the linear part is zero.

EXTQUAD: the hessian of this block and the linear part is non-zero.

LIN: the hessian is zero.

Enumerator:

LIN
QUAD
EXTQUAD

Definition at line 112 of file dualqqp.h.

Constructor & Destructor Documentation

QqpDualFunc::QqpDualFunc	(	MinlpProblem &	qqp_,
		Param &	param_,
		Pointer< ostream >	out_func_p_ = `out_out_p`,
		Pointer< ostream >	out_func_log_p_ = `out_log_p`
	)			`[inline]`

Constructor for a MinlpReform and a shift.

Parameters:

	qqp_	The MinlpReform, the DualFunc consists of.
	param_	Parameters.
	out_func_p_	A pointer to an output stream for function output.
	out_func_log_p_	A pointer to an output stream for function logging output.

Definition at line 334 of file dualqqp.h.

Member Function Documentation

int QqpDualFunc::num_qbox ( ) const [inline, protected]

The number of quadratic-box-constraints.

Returns:: The number of quadratic-box-constraints.

Definition at line 237 of file dualqqp.h.

int QqpDualFunc::num_blocks ( ) const [inline, protected]

The number of blocks.

Returns:: The number of blocks.

Definition at line 242 of file dualqqp.h.

void QqpDualFunc::init_ext ( ) [protected]

Check's, if partial Lagrange problem is extended Set ext[k] to true, if the bounds are not symmetric or no linear part exists.

Or you say: Check, if modified b_k's are zero.

See also:: ext

void QqpDualFunc::init ( ) [protected]

Initialization of the dual function.

Allocating memory, setting counters to zero, computing u,W...

Check's, whether the Lagrange problem is extended by calling init_ext().

Set's the modified c,b-values by calling set_bc(). Set's the ball-constraint type by calling set_ball_con(lower, upper).

See also:: init_ext(); set_bc(); set_ball_con()

void QqpDualFunc::set_ball_con ( ) [protected]

Initialize the ball constraints.

Initialize the ball constraints for each block with the corresponding part of lower and upper. Set's the type of each ball-constraint to true, if it contains one not-discrete variable.

See also:: ball_con

void QqpDualFunc::get_bc	(	double &	c_,
		dvector &	b_,
		SepQcFunc &	q
	)			`[protected]`

Compute's modified b,c values for a SepQcFunc.

Sums mid_point[k]*q.A[k]*mid_point[k] + q.b[k]*mid_point[k] over all blocks. Adds the constant part of q: q.c

Parameters:

	c_	The modified c-value.
	b_	The modified b-value.
	q	The SepQcfunc to compute.

void QqpDualFunc::set_bc ( ) [protected]

Initialize the modified b,c-values.

Computes for each constraint and the objective the modified b,c-values by calling get_bc.

See also:: get_bc(double&, dvector&, SepQcFunc&); b_con; b_obj; c_con; c_obj

int QqpDualFunc::set_dual_val ( ) const [protected]

Compute the value of the dual function.

The function value is stored in dual_val.

See also:: dual_val

Returns:: Sum of return codes from the eigenvalue computation.

double QqpDualFunc::eval_mod_con ( int con_nr ) const [protected]

Evaluates a modified constraint.

Parameters:

con_nr

The number of the constraint to evaluate.

Returns:: The value of the constraint.

double QqpDualFunc::eval_mod_obj ( ) const [protected]

Evaluates the modified objective.

Returns:: The value of the objective.

void QqpDualFunc::set_subgrad ( ) const [protected]

Compute a subgradient of the dual function.

The subgradient is stored in subgrad.

See also:: eval_mod_con(int); subgrad

virtual int QqpDualFunc::valgrad	(	double &	val,
		UserVector< double > &	g,
		const UserVector< double > &	z
	)			const `[virtual]`

Evaluates the function value and computes the subgradient of the dual function.

Parameters:

	val	A double to store the value in.
	g	A dvector to store the subgradient in.
	z	The dual value to compute the value and subgradient for.

Returns:: Return code from set_dual_val().

See also:: set_dual_val(); set_subgrad()

Reimplemented from Func.

double QqpDualFunc::eval ( const UserVector< double > & z ) const [inline, virtual]

Evaluates this function for a dvector.

Sets dual_point to given point and calls set_dual_val(). This method doesn't look at the return value from set_dual_val() !

Parameters:

z

The dvector to compute the value for.

Returns:: The value of this function.

See also:: valgrad(double&, dvector&, dvector&)

Implements Func.

Definition at line 364 of file dualqqp.h.

void QqpDualFunc::grad	(	UserVector< double > &	g,
		const UserVector< double > &	x
	)			const `[inline, virtual]`

Computes the gradient of this function.

Calls valgrad(). This method doesn't look at the return value from set_dual_val(), so use valgrad() instead !

Parameters:

	g	The dvector to store the gradient in.
	x	The dvector to compute the gradient for.

Implements Func.

Definition at line 389 of file dualqqp.h.

virtual void QqpDualFunc::HessMult	(	UserVector< double > &	y,
		const UserVector< double > &	x,
		const UserVector< double > &	z
	)			const `[inline, virtual]`

Does nothing.

Should do: Compute the product of the Hessian and a dvector.

Parameters:

	y	The dvector to store the result in.
	x	The dvector to evaluate the Hessian for.
	z	The dvector to multiply with the Hessian. Does nothing.

Implements Func.

Definition at line 406 of file dualqqp.h.

dvector QqpDualFunc::get_dual_point ( ) const [virtual]

Set the Lagrange multipliers of the quadratic box constraints.

The last dual point of the original qqp.

Returns:: The dual point of the not-extended(!) QQP, used in the last iteration.

Implements DualFunc.

dvector QqpDualFunc::get_dual_point ( dvector & ext_dual_point ) const [inline]

The dual point of the original qqp for an extended dual point.

If the extended dual point (the one, you can use for eval()) is not equal to dual_point, eval(ext_dual_point) is called. Then get_dual_point() is called.

Parameters:

ext_dual_point

A dual point from the extended qqp.

See also:: get_dual_point()

Definition at line 425 of file dualqqp.h.

double QqpDualFunc::get_dual_val ( ) const [inline, virtual]

The last dual value.

Returns:: The dual value, used in the last iteration.

Implements DualFunc.

Definition at line 433 of file dualqqp.h.

double QqpDualFunc::get_dual_val ( dvector & ext_dual_point ) const [inline]

The dual value for an extended dual point.

If the extended dual point (the one, you can use for eval()) is not equal to dual_point, eval(ext_dual_point) is called. Then get_dual_val() is called.

Parameters:

ext_dual_point

A dual point from the extended qqp.

See also:: get_dual_val()

Definition at line 441 of file dualqqp.h.

dvector QqpDualFunc::get_orig_point ( int use_eig_vec = 0 ) const [virtual]

Gives the solution point of the Lagrangian function.

Parameters:

use_eig_vec

The eigenvector to use to compute the lag-point.

Returns:: The solution point of the Lagrangian function, used in the last iteration.

Implements DualFunc.

dvector QqpDualFunc::get_orig_point	(	dvector &	ext_dual_point,
		int	use_eig_vec = `0`
	)			const `[inline]`

The dual value for an extended dual point.

If the extended dual point (the one, you can use for eval()) is not equal to dual_point, eval(ext_dual_point) is called. Then get_orig_point() is called.

Parameters:

ext_dual_point

A dual point from the extended qqp.

See also:: get_orig_point()

Definition at line 458 of file dualqqp.h.

int QqpDualFunc::nr_of_orig_points ( ) const [inline, virtual]

The number of eigenvectors, which are computed in each evaluation.

Returns:: The size of eig_vec.

Reimplemented from DualFunc.

Definition at line 466 of file dualqqp.h.

void QqpDualFunc::print ( ostream & out ) const [virtual]

Print's a lot of information about this function.

Parameters:

out

The ostream to print to.

Reimplemented from Func.

Friends And Related Function Documentation

friend class QqpMatrix [friend]

Definition at line 101 of file dualqqp.h.

friend class QqpExtMatrix [friend]

Definition at line 102 of file dualqqp.h.

Member Data Documentation

vector<b_type> QqpDualFunc::block_type [protected]

Indicates for each block, which type the block of the lagrange problem has.

QUAD, EXTQUAD or LIN. Initialized in init_ext.

See also:: init_ext(); init()

Definition at line 120 of file dualqqp.h.

ivector QqpDualFunc::i_ext [protected]

The indices of the new quadratic box constraints.

Definition at line 124 of file dualqqp.h.

int QqpDualFunc::num_ext [protected]

The number of extended blocks.

Definition at line 128 of file dualqqp.h.

ivector QqpDualFunc::i_q [protected]

The index of the start of the quadratric box constraints for the k-th block.

Size of i_q: number of nonlinear-blocks.

Definition at line 133 of file dualqqp.h.

int QqpDualFunc::n_q [protected]

The number of quadratic variables.

Definition at line 137 of file dualqqp.h.

dvector QqpDualFunc::mid_point [protected]

The mid point of the box = 0.5*(lower+upper).

Initialized in init, should be deleted.

See also:: init()

Definition at line 143 of file dualqqp.h.

BlockMatrix QqpDualFunc::W [protected]

The half-length of the edges of the box.

Initialized in init as BlockMatrix of DiagMatrix-blocks.

See also:: init()

Definition at line 149 of file dualqqp.h.

dvector QqpDualFunc::radius [protected]

The radius of the ball-constraints.

Definition at line 153 of file dualqqp.h.

vector<bool> QqpDualFunc::ball_con [protected]

The type of the ball-constraints.

False if equality constraint and true if inequality constraint. Initialized in set_ball_con.

See also:: set_ball_con(); init()

Definition at line 161 of file dualqqp.h.

vector<dvector> QqpDualFunc::b_con [protected]

The type of scaling (currently not used).

True if scaling and false else. Initialized in set_ball_con.

See also:: set_ball_con(); init() The modified b-values for the constraints. Size set and initialized in set_bc.; set_bc()

Definition at line 175 of file dualqqp.h.

dvector QqpDualFunc::b_obj [protected]

The modified b-value for the objective-function.

Set in set_bc.

See also:: set_bc()

Definition at line 181 of file dualqqp.h.

dvector QqpDualFunc::c_con [protected]

The modified c-values for the constraints.

Size set and initialized in set_bc.

See also:: set_bc()

Definition at line 187 of file dualqqp.h.

double QqpDualFunc::c_obj [protected]

The modified c-value for the objective-function.

Set in set_bc.

See also:: set_bc()

Definition at line 193 of file dualqqp.h.

vector<Pointer<UserMatrix> > QqpDualFunc::A_lag [protected]

The block matrices of the modified Lagrangian Set in init.

See also:: init()

Definition at line 199 of file dualqqp.h.

vector<dvector> QqpDualFunc::b_lag [mutable, protected]

The linear part of the modified Lagrangian Set in init.

See also:: set_dual_val()

Definition at line 205 of file dualqqp.h.

double QqpDualFunc::c_lag [mutable, protected]

The constant part of the modified Lagrangian Set in init.

See also:: set_dual_val()

Definition at line 211 of file dualqqp.h.

dvector QqpDualFunc::x_lag [mutable, protected]

The Lagrange solution.

See also:: set_subgrad()

Definition at line 216 of file dualqqp.h.

double QqpDualFunc::dual_val [mutable, protected]

current value of the dual function.

Definition at line 220 of file dualqqp.h.

dvector QqpDualFunc::subgrad [mutable, protected]

The subgradient.

Definition at line 224 of file dualqqp.h.

vector<vector<double> > QqpDualFunc::eig_val [mutable, protected]

minimal eigenvalues of A_lag[k], k=0,.

.,block_size-1. eig_val[k] are the first eig_val[k].size() eigenvalues of the k'th block, starting with the smallest.

Definition at line 228 of file dualqqp.h.

vector<vector<dvector> > QqpDualFunc::eig_vec [mutable, protected]

eigenvectors of A_lag[k], k=0,.

.,block_size-1. eig_vec[k] are the first eig_vec[k].size() eigenvectors of the k'th block, starting with the one, belong to the smallest eigenvalue.

Definition at line 232 of file dualqqp.h.

int QqpDualFunc::num_matmult

number of matrix vector multiplications

Definition at line 318 of file dualqqp.h.

double QqpDualFunc::eig_time [mutable]

time spent by the eigenvalue calculation

Definition at line 320 of file dualqqp.h.

dvector QqpDualFunc::dual_point [mutable]

The dual variables of the extended (!) dual function.

This is the dual point, which was last used to evaluate the function.

See also:: get_dual_point()

Definition at line 326 of file dualqqp.h.

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

dualqqp.h

QqpDualFunc Class Reference

Public Member Functions

Public Attributes

Protected Types

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation