Convexify Class Reference

Class to convexify a (decomposed) function. More...

#include <relax.h>

Collaboration diagram for Convexify:

Public Member Functions
	Convexify (Pointer< Param > param_)
void	new_sampleset (UserVector< double > &lower, UserVector< double > &upper, SepQcFunc &f)
	Computes a new sample set for the nonlinear blocks of a function.
double	convexify (SepQcFunc &f, bool eq, vector< double > &min_eigval, vector< double > &max_eigval, UserVector< double > &lower, UserVector< double > &upper)
	Computes the cgu or alpha parameters for a function.
void	get_decomposed_functions (pair< Pointer< SepQcFunc >, Pointer< SepQcFunc > > &f)
	Gives a convexified function.
void	check_convex2 (vector< double > &min_eigval, vector< double > &max_eigval, SepQcFunc &f, const vector< vector< dvector > > &sample_set)
void	check_convexification (MinlpProblem &conv_prob, MinlpProblem &orig_prob, const ivector &ineq_index, int test_pts=20)
	Checks, if a problem is a convex relaxation of another problem.
Public Attributes
vector< pair< double, double > >	convexify_c
	Constant parts, generated by alpha or cgu.
map< int, double >	characteristica1
	The shifting parameters which characterize the latest convexification.
map< int, double >	characteristica2
Private Member Functions
void	convexify_cgu (SepQcFunc &f, int k)
	Computes the cgu-parameters for the convexification of the k'th block of f.
pair< double, double >	convexify_alpha (SepQcFunc &f, int k, const dvector &low, const dvector &up, Pointer< set< int > > i_quad, Pointer< set< int > > i_nonquadlin)
	Computes the alpha-parameters for the convexification of the k'th block of f.
pair< double, double >	convexify_alpha (SepQcFunc &f, int k, const dvector &low, const dvector &up)
pair< double, double >	convexify_alpha2 (SepQcFunc &f, int k, const dvector &low, const dvector &up)
Private Attributes
Pointer< Param >	param
Sampling	sampling
	Object to generate sample points.
vector< vector< dvector > >	sample_set
Decomposition	decomp
double	very_large
double	cgu_eps
pair< Pointer< UserVector < double > >, Pointer < UserVector< double > > >	convexify_a
	Diagonal of matrices, generated by alpha or cgu method.
pair< Pointer< UserVector < double > >, Pointer < UserVector< double > > >	convexify_b
	Linear parts, generated by alpha or cgu method.
vector< bool >	convexified_by_cgu
	Indicates, whether the last function was convexified with the cgu method.

Detailed Description

Class to convexify a (decomposed) function.

Parameters:

	Relax	very large options double default 1E+99 Determines, when we use CGU and when we use the alpha-method to convexify a function. If ${}{} < -very$, we use CGU, else we try alpha. If the norm of the computed alpha is > very, we use also CGU.
	Relax	CGU epsilon options double $$ default 0. An epsilon, which is added to each constraint in the LP, we solve when we compute a CGU.

Definition at line 33 of file relax.h.

Constructor & Destructor Documentation

Convexify::Convexify ( Pointer< Param > param_ ) [inline]

Definition at line 80 of file relax.h.

Member Function Documentation

void Convexify::convexify_cgu	(	SepQcFunc &	f,
		int	k
	)			`[private]`

Computes the cgu-parameters for the convexification of the k'th block of f.

Parameters:

	f	The function to convexify.
	k	The block number.

pair<double, double> Convexify::convexify_alpha	(	SepQcFunc &	f,
		int	k,
		const dvector &	low,
		const dvector &	up,
		Pointer< set< int > >	i_quad,
		Pointer< set< int > >	i_nonquadlin
	)			`[private]`

Computes the alpha-parameters for the convexification of the k'th block of f.

Parameters:

	f	The function to convexify.
	k	The block number.
	low	Lower bounds for the k'th block.
	up	Upper bounds for the k'th block.

pair<double, double> Convexify::convexify_alpha	(	SepQcFunc &	f,
		int	k,
		const dvector &	low,
		const dvector &	up
	)			`[private]`

pair<double, double> Convexify::convexify_alpha2	(	SepQcFunc &	f,
		int	k,
		const dvector &	low,
		const dvector &	up
	)			`[private]`

void Convexify::new_sampleset	(	UserVector< double > &	lower,
		UserVector< double > &	upper,
		SepQcFunc &	f
	)

Computes a new sample set for the nonlinear blocks of a function.

Parameters:

	lower	Lower bounds of variables.
	upper	Upper bounds of variables.
	f	The function, which block-structure we use.

double Convexify::convexify	(	SepQcFunc &	f,
		bool	eq,
		vector< double > &	min_eigval,
		vector< double > &	max_eigval,
		UserVector< double > &	lower,
		UserVector< double > &	upper
	)

Computes the cgu or alpha parameters for a function.

Parameters:

	f	The function.
	eq	Indicates, whether also the parameters for -f should be computed.
	min_eigval	The minimum eigenvalues for the hessians of each block of f.
	max_eigval	The maximum eigenvalues for the hessians of each block of f.
	convex	Indicates, whether f is convex.
	concave	Indicates, whether f is concave.
	lower	Lower bounds of variables.
	upper	Upper bounds of variables.

void Convexify::get_decomposed_functions ( pair< Pointer< SepQcFunc >, Pointer< SepQcFunc > > & f )

Gives a convexified function.

Gives the convexified function in it's decomposed form (the form, which was used in convexify).

Parameters:

f

A pair, where ew can store the convexified f and (sometimes) -f in. At the beginning, it needs to hold the decomposed f at first place, the second needs to empty.

void Convexify::check_convex2	(	vector< double > &	min_eigval,
		vector< double > &	max_eigval,
		SepQcFunc &	f,
		const vector< vector< dvector > > &	sample_set
	)

void Convexify::check_convexification	(	MinlpProblem &	conv_prob,
		MinlpProblem &	orig_prob,
		const ivector &	ineq_index,
		int	test_pts = `20`
	)

Checks, if a problem is a convex relaxation of another problem.

Checks, if the minimum eigenvalues of the convexified functions are >=0. Checks, if the function values of the convexified functions are lower than the value of the original functions.

Parameters: