class sum, $\sum_{i=1}^n f_i(x)$ More...

#include <CouenneExprSum.hpp>

Inheritance diagram for Couenne::exprSum:

Collaboration diagram for Couenne::exprSum:

Public Member Functions
	exprSum (expression **=NULL, int=0)
	Constructors, destructor. More...

	exprSum (expression , expression )
	Constructor with two elements. More...

virtual	~exprSum ()
	Empty destructor. More...

virtual expression *	clone (Domain *d=NULL) const
	Cloning method. More...

std::string	printOp () const
	Print operator. More...

virtual CouNumber	operator() ()
	Function for the evaluation of the expression. More...

virtual expression *	differentiate (int index)
	Differentiation. More...

virtual expression *	simplify ()
	Simplification. More...

virtual int	Linearity ()
	Get a measure of "how linear" the expression is: More...

virtual void	getBounds (expression &, expression &)
	Get lower and upper bound of an expression (if any) More...

virtual void	getBounds (CouNumber &, CouNumber &)
	Get lower and upper bound of an expression (if any) More...

virtual exprAux *	standardize (CouenneProblem *p, bool addAux=true)
	Reduce expression in standard form, creating additional aux variables (and constraints) More...

virtual void	generateCuts (expression , OsiCuts &, const CouenneCutGenerator , t_chg_bounds *=NULL, int=-1, CouNumber=-COUENNE_INFINITY, CouNumber=COUENNE_INFINITY)
	Special version for linear constraints. More...

virtual enum expr_type	code ()
	Code for comparison. More...

virtual bool	impliedBound (int, CouNumber , CouNumber , t_chg_bounds *, enum auxSign=expression::AUX_EQ)
	Implied bound. More...

exprAux *	createQuadratic (CouenneProblem *)
	Checks for quadratic terms in the expression and returns an exprQuad if there are enough to create something that can be convexified. More...

Public Member Functions inherited from Couenne::exprOp
virtual enum nodeType	Type () const
	Node type. More...

	exprOp (expression **arglist, int nargs)
	Constructor. More...

	exprOp (expression arg0, expression arg1)
	Constructor with two arguments (for convenience) More...

virtual	~exprOp ()
	Destructor. More...

	exprOp (const exprOp &e, Domain *d=NULL)
	Copy constructor: only allocate space for argument list, which will be copied with clonearglist() More...

expression **	ArgList () const
	return argument list More...

virtual void	ArgList (expression **al)
	set arglist (used in deleting nodes without deleting children) More...

int	nArgs () const
	return number of arguments More...

virtual void	print (std::ostream &out=std::cout, bool=false) const
	I/O. More...

virtual enum pos	printPos () const
	print position (PRE, INSIDE, POST) More...

virtual int	DepList (std::set< int > &deplist, enum dig_type type=ORIG_ONLY)
	fill in the set with all indices of variables appearing in the expression More...

expression **	clonearglist (Domain *d=NULL) const
	clone argument list (for use with clone method) More...

int	shrink_arglist (CouNumber, CouNumber)
	compress argument list More...

virtual bool	isInteger ()
	is this expression integer? More...

virtual int	compare (exprOp &)
	compare with other generic exprOp More...

virtual int	rank ()
	used in rank-based branching variable choice More...

virtual void	fillDepSet (std::set< DepNode , compNode > dep, DepGraph *g)
	fill in dependence structure update dependence set with index of this variable More...

virtual void	replace (exprVar , exprVar )
	replace variable with other More...

virtual void	realign (const CouenneProblem *p)
	empty function to redirect variables to proper variable vector More...

Public Member Functions inherited from Couenne::expression
	expression ()
	Constructor. More...

	expression (const expression &e, Domain *d=NULL)
	Copy constructor. More...

virtual	~expression ()
	Destructor. More...

virtual int	Index () const
	Return index of variable (only valid for exprVar and exprAux) More...

virtual expression *	Argument () const
	return argument (when applicable, i.e., with univariate functions) More...

virtual expression **	ArgPtr ()
	return pointer to argument (when applicable, i.e., with univariate functions) More...

virtual expression *	Image () const
	return pointer to corresponding expression (for auxiliary variables only) More...

virtual void	Image (expression *image)
	set expression associated with this auxiliary variable (for compatibility with exprAux) More...

virtual CouNumber	Value () const
	value (empty) More...

virtual const expression *	Original () const
	If this is an exprClone of a exprClone of an expr???, point to the original expr??? instead of an exprClone – improve computing efficiency. More...

virtual CouNumber	gradientNorm (const double *x)
	return l-2 norm of gradient at given point More...

virtual int	dependsOn (int *ind, int n, enum dig_type type=STOP_AT_AUX)
	dependence on variable set: return cardinality of subset of the set of indices in first argument which occur in expression. More...

int	dependsOn (int singleton, enum dig_type type=STOP_AT_AUX)
	version with one index only More...

virtual bool	isDefinedInteger ()
	is this expression defined as an integer? More...

virtual enum convexity	convexity () const
	either CONVEX, CONCAVE, AFFINE, or NONCONVEX More...

virtual int	compare (expression &)
	compare expressions More...

virtual int	compare (exprCopy &)
	compare copies of expressions More...

virtual int	Multiplicity ()
	multiplicity of a variable More...

virtual CouNumber	selectBranch (const CouenneObject obj, const OsiBranchingInformation info, expression &var, double &brpts, double *&brDist, int &way)
	set up branching object by evaluating many branching points for each expression's arguments. More...

virtual void	linkDomain (Domain *d)
	empty function to update domain pointer More...

virtual bool	isBijective () const
	indicating if function is monotonically increasing More...

virtual CouNumber	inverse (expression *vardep) const
	compute the inverse function More...

virtual void	closestFeasible (expression varind, expression vardep, CouNumber &left, CouNumber &right) const
	closest feasible points in function in both directions More...

virtual bool	isCuttable (CouenneProblem *problem, int index) const
	can this expression be further linearized or are we on its concave ("bad") side More...

virtual bool	isaCopy () const
	return true if this is a copy of something (i.e. an exprCopy) More...

virtual expression *	Copy () const
	return copy of this expression (only makes sense in exprCopy) More...

Protected Member Functions
int	impliedBoundSum (CouNumber wl, CouNumber wu, std::vector< CouNumber > &xl, std::vector< CouNumber > &xu, std::vector< std::pair< int, CouNumber > > &nl, std::vector< std::pair< int, CouNumber > > &nu)
	inferring bounds on factors of a product More...

Additional Inherited Members
Public Types inherited from Couenne::expression
enum	auxSign { AUX_UNDEF =-2, AUX_LEQ =-1, AUX_EQ, AUX_GEQ }
	"sign" of the constraint defining an auxiliary. More...

Protected Attributes inherited from Couenne::exprOp
expression **	arglist_
	argument list is an array of pointers to other expressions More...

int	nargs_
	number of arguments (cardinality of arglist) More...

Detailed Description

class sum, $\sum_{i=1}^n f_i(x)$

Definition at line 22 of file CouenneExprSum.hpp.

Constructor & Destructor Documentation

exprSum::exprSum	(	expression **	al = `NULL`,
		int	n = `0`
	)

Constructors, destructor.

Constructor.

Definition at line 20 of file exprSum.cpp.

exprSum::exprSum	(	expression *	arg0,
		expression *	arg1
	)

Constructor with two elements.

Copy constructor.

Definition at line 36 of file exprSum.cpp.

virtual Couenne::exprSum::~exprSum ( )

inlinevirtual

Empty destructor.

Definition at line 33 of file CouenneExprSum.hpp.

Member Function Documentation

virtual expression* Couenne::exprSum::clone ( Domain * d = NULL ) const

inlinevirtual

Cloning method.

Reimplemented from Couenne::expression.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 36 of file CouenneExprSum.hpp.

std::string Couenne::exprSum::printOp ( ) const

inlinevirtual

Print operator.

Reimplemented from Couenne::exprOp.

Definition at line 40 of file CouenneExprSum.hpp.

CouNumber Couenne::exprSum::operator() ( )

inlinevirtual

Function for the evaluation of the expression.

compute sum

Implements Couenne::expression.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 118 of file CouenneExprSum.hpp.

expression * exprSum::differentiate ( int index )

virtual

Differentiation.

differentiate sum of expressions

Reimplemented from Couenne::expression.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 97 of file exprSum.cpp.

expression * exprSum::simplify ( )

virtual

Simplification.

simplify sums

Reimplemented from Couenne::exprOp.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 51 of file exprSum.cpp.

int exprSum::Linearity ( )

virtual

Get a measure of "how linear" the expression is:

get a measure of "how linear" the expression is (see CouenneTypes.h)

Reimplemented from Couenne::exprOp.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 147 of file exprSum.cpp.

void exprSum::getBounds	(	expression *&	lb,
		expression *&	ub
	)

virtual

Get lower and upper bound of an expression (if any)

Reimplemented from Couenne::expression.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 118 of file exprSum.cpp.

void exprSum::getBounds	(	CouNumber &	lb,
		CouNumber &	ub
	)

virtual

Get lower and upper bound of an expression (if any)

Reimplemented from Couenne::expression.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 132 of file exprSum.cpp.

exprAux * exprSum::standardize	(	CouenneProblem *	p,
		bool	addAux = `true`
	)

virtual

Reduce expression in standard form, creating additional aux variables (and constraints)

translate a sum/difference/exprOpp into:

1) an exprGroup, if only linear terms are present 2) an exprQuad, if some quadratic/bilinear terms exist

Reimplemented from Couenne::exprOp.

Definition at line 28 of file sumStandardize.cpp.

void exprSum::generateCuts	(	expression *	w,
		OsiCuts &	cs,
		const CouenneCutGenerator *	cg,
		t_chg_bounds *	chg = `NULL`,
		int	wind = `-1`,
		CouNumber	lb = `-COUENNE_INFINITY`,
		CouNumber	ub = `COUENNE_INFINITY`
	)

virtual

Special version for linear constraints.

first, make room for aux variable

scan arglist for (aux) variables and constants

added only once, it is global

Reimplemented from Couenne::expression.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 24 of file conv-exprSum.cpp.

virtual enum expr_type Couenne::exprSum::code ( )

inlinevirtual

Code for comparison.

Reimplemented from Couenne::exprOp.

Reimplemented in Couenne::exprQuad, and Couenne::exprGroup.

Definition at line 73 of file CouenneExprSum.hpp.

bool exprSum::impliedBound	(	int	wind,
		CouNumber *	l,
		CouNumber *	u,
		t_chg_bounds *	chg,
		enum auxSign	sign = `expression::AUX_EQ`
	)

virtual

Implied bound.

implied bound processing for expression w = x+y+t+..., upon change in lower- and/or upper bound of w, whose index is wind

An expression

$w = a0 + \sum_{i\in I1} a_i x_i + \sum_{i\in I2} a_i x_i$

is given such that all $a_i$ are positive for $i \in I1$ and negative for $i \in I2$ . If the bounds on $w \in [l,u]$ , implied bounds on all $x_i, i\in I1 \cup I2$ are as follows:

$\forall i\in I1$ $x_i \ge (l - a0 - \sum_{j\in I1 | j\neq i} a_j u_j - \sum_{j\in I2} a_j l_j) / a_i$ $x_i \le (u - a0 - \sum_{j\in I1 | j\neq i} a_j l_j - \sum_{j\in I2} a_j u_j) / a_i$

$\forall i\in I2$ $x_i \ge (u - a0 - \sum_{j\in I1} a_j u_j - \sum_{j\in I2 | j\neq i} a_j l_j) / a_i$ $x_i \le (l - a0 - \sum_{j\in I1} a_j l_j - \sum_{j\in I2 | j\neq i} a_j u_j) / a_i$ ,

where $l_i$ and $u_i$ are lower and upper bound, respectively, of $x_i$ . We also have to check if some of these bounds are infinite.

An expression

$w = a0 + \sum_{i\in I1} a_i x_i + \sum_{i\in I2} a_i x_i$

is given such that all $a_i$ are positive for $i I1$ and negative for $i in I2$. If the bounds on $w [l,b]$, implied bounds on all $x_i, i I1 I2$ are as follows:

$\forall i\in I1$

$x_i \ge (l - a0 - sum_{j\in I1 | j\neq i} a_j u_j - sum_{j\in I2} a_j l_j) / a_i$ $x_i \le (u - a0 - sum_{j\in I1 | j\neq i} a_j l_j - sum_{j\in I2} a_j u_j) / a_i$

$\forall i\in I2$

$x_i \ge (u - a0 - sum_{j\in I1} a_j u_j - sum_{j\in I2 | j\neq i} a_j l_j) / a_i$ $x_i \le (l - a0 - sum_{j\in I1} a_j l_j - sum_{j\in I2 | j\neq i} a_j u_j) / a_i$ ,

where $l_i$ and $u_i$ are lower and upper bound, respectively, of $x_i$ . We also have to check if some of these bounds are infinite.

Reimplemented from Couenne::expression.

Reimplemented in Couenne::exprQuad.

Definition at line 26 of file impliedBounds-exprSum.cpp.

exprAux* Couenne::exprSum::createQuadratic ( CouenneProblem * )

Checks for quadratic terms in the expression and returns an exprQuad if there are enough to create something that can be convexified.

int exprSum::impliedBoundSum	(	CouNumber	wl,
		CouNumber	wu,
		std::vector< CouNumber > &	xl,
		std::vector< CouNumber > &	xu,
		std::vector< std::pair< int, CouNumber > > &	nl,
		std::vector< std::pair< int, CouNumber > > &	nu
	)

protected

inferring bounds on factors of a product

Definition at line 20 of file impliedBounds-sum.cpp.

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

/tmp/OS-2.10.2/Couenne/src/expression/operators/CouenneExprSum.hpp
/tmp/OS-2.10.2/Couenne/src/bound_tightening/operators/impliedBounds-exprSum.cpp
/tmp/OS-2.10.2/Couenne/src/bound_tightening/operators/impliedBounds-sum.cpp
/tmp/OS-2.10.2/Couenne/src/convex/operators/conv-exprSum.cpp
/tmp/OS-2.10.2/Couenne/src/expression/operators/exprSum.cpp
/tmp/OS-2.10.2/Couenne/src/standardize/sumStandardize.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation