Class to handle parameterized quadratic programs(QP) More...

#include <games.h>

Inheritance diagram for Game::QP_Param:

Public Member Functions
	QP_Param (GRBEnv *env=nullptr)
	Initialize only the size. Everything else is empty (can be updated later) More...

	QP_Param (arma::sp_mat Q, arma::sp_mat C, arma::sp_mat A, arma::sp_mat B, arma::vec c, arma::vec b, GRBEnv *env=nullptr)
	Set data at construct time. More...

	QP_Param (const QP_Param &Qu)
	Copy constructor. More...

QP_Param &	set (const arma::sp_mat &Q, const arma::sp_mat &C, const arma::sp_mat &A, const arma::sp_mat &B, const arma::vec &c, const arma::vec &b) final
	Setting the data, while keeping the input objects intact. More...

QP_Param &	set (arma::sp_mat &&Q, arma::sp_mat &&C, arma::sp_mat &&A, arma::sp_mat &&B, arma::vec &&c, arma::vec &&b) final
	Faster means to set data. But the input objects might be corrupted now. More...

QP_Param &	set (const QP_objective &obj, const QP_constraints &cons) final

QP_Param &	set (QP_objective &&obj, QP_constraints &&cons) final

bool	operator== (const QP_Param &Q2) const

unsigned int	KKT (arma::sp_mat &M, arma::sp_mat &N, arma::vec &q) const
	Compute the KKT conditions for the given QP. More...

std::unique_ptr< GRBModel >	solveFixed (arma::vec x)

double	computeObjective (const arma::vec &y, const arma::vec &x, bool checkFeas=true, double tol=1e-6) const

bool	is_Playable (const QP_Param &P) const

QP_Param &	addDummy (unsigned int pars, unsigned int vars=0, int position=-1) override

void	write (std::string filename, bool append) const
	Writes a given parameterized Mathematical program to a set of files. More...

void	save (std::string filename, bool erase=true) const
	Saves the `Game::QP_Param` object in a loadable file. More...

long int	load (std::string filename, long int pos=0)
	Loads the `Game::QP_Param` object stored in a file. More...

void	bound (double bigM, unsigned int primals)

arma::sp_mat	getQ () const
	Read-only access to the private variable Q. More...

arma::sp_mat	getC () const
	Read-only access to the private variable C. More...

arma::sp_mat	getA () const
	Read-only access to the private variable A. More...

arma::sp_mat	getB () const
	Read-only access to the private variable B. More...

arma::vec	getc () const
	Read-only access to the private variable c. More...

arma::vec	getb () const
	Read-only access to the private variable b. More...

unsigned int	getNx () const
	Read-only access to the private variable Nx. More...

unsigned int	getNy () const
	Read-only access to the private variable Ny. More...

MP_Param &	setQ (const arma::sp_mat &Q)
	Set the private variable Q. More...

MP_Param &	setC (const arma::sp_mat &C)
	Set the private variable C. More...

MP_Param &	setA (const arma::sp_mat &A)
	Set the private variable A. More...

MP_Param &	setB (const arma::sp_mat &B)
	Set the private variable B. More...

MP_Param &	setc (const arma::vec &c)
	Set the private variable c. More...

MP_Param &	setb (const arma::vec &b)
	Set the private variable b. More...

Static Public Member Functions
static bool	dataCheck (const QP_objective &obj, const QP_constraints &cons, bool checkObj=true, bool checkCons=true)

Protected Member Functions
unsigned int	size ()
	Calculates `Nx`, `Ny` and `Ncons` Computes parameters in MP_Param: More...

bool	dataCheck (bool forcesymm=true) const
	Check that the data for the MP_Param class is valid Always works after calls to MP_Param::size() Checks that are done: More...

virtual bool	finalize ()
	Finalize the MP_Param object. More...

Protected Attributes
arma::sp_mat	Q

arma::sp_mat	A

arma::sp_mat	B

arma::sp_mat	C

arma::vec	c

arma::vec	b

unsigned int	Nx

unsigned int	Ny

unsigned int	Ncons

Private Member Functions
int	make_yQy ()
	Adds the Gurobi Quadratic objective to the Gurobi model `QuadModel`. More...

Private Attributes
GRBEnv *	env

GRBModel	QuadModel

bool	made_yQy

Detailed Description

Class to handle parameterized quadratic programs(QP)

Represents a Parameterized QP as

$\min_y \frac{1}{2}y^TQy + c^Ty + (Cx)^T y$

Subject to

$\begin{eqnarray} Ax + By &\leq& b \\ y &\geq& 0 \end{eqnarray}$

Definition at line 146 of file games.h.

Constructor & Destructor Documentation

◆ QP_Param() [1/3]

Game::QP_Param::QP_Param ( GRBEnv * env = nullptr )

inline

Initialize only the size. Everything else is empty (can be updated later)

Definition at line 169 of file games.h.

◆ QP_Param() [2/3]

Game::QP_Param::QP_Param	(	arma::sp_mat	Q,
		arma::sp_mat	C,
		arma::sp_mat	A,
		arma::sp_mat	B,
		arma::vec	c,
		arma::vec	b,
		GRBEnv *	env = `nullptr`
	)

inline

Set data at construct time.

Definition at line 175 of file games.h.

◆ QP_Param() [3/3]

Game::QP_Param::QP_Param ( const QP_Param & Qu )

inline

Copy constructor.

Definition at line 186 of file games.h.

Member Function Documentation

◆ addDummy()

Game::QP_Param & Game::QP_Param::addDummy	(	unsigned int	pars,
		unsigned int	vars = `0`,
		int	position = `-1`
	)

overridevirtual

Warning: You might have to rerun QP_Param::KKT since you have now changed the QP.; This implies you might have to rerun NashGame::FormulateLCP again too.

Reimplemented from Game::MP_Param.

Definition at line 386 of file Games.cpp.

◆ bound()

void Game::MP_Param::bound	(	double	bigM,
		unsigned int	primals
	)

inherited

◆ computeObjective()

double Game::QP_Param::computeObjective	(	const arma::vec &	y,
		const arma::vec &	x,
		bool	checkFeas = `true`,
		double	tol = `1e-6`
	)		const

Computes the objective value, given a vector y and a parameterizing vector x

Computes $\frac{1}{2} y^TQy + (Cx)^Ty$ given the input values y and x.

Parameters

checkFeas if true, checks if the given satisfies the constraints of the problem, namely $Ax + By \leq b$ .

Definition at line 490 of file Games.cpp.

◆ dataCheck() [1/2]

bool Game::MP_Param::dataCheck ( bool forcesymm = true ) const

protectedinherited

Check that the data for the MP_Param class is valid Always works after calls to MP_Param::size() Checks that are done:

Number of columns in Q is same as Ny (Q should be square)
Number of columns of A should be Nx
Number of columns of B should be Ny
Number of rows in C should be Ny
Size of c should be Ny
A and B should have the same number of rows, equal to Ncons
if forcesymm is true, then Q should be symmetric

Returns: true if all above checks are cleared. false otherwise.

Definition at line 219 of file Games.cpp.

◆ dataCheck() [2/2]

bool Game::MP_Param::dataCheck	(	const QP_objective &	obj,
		const QP_constraints &	cons,
		bool	checkObj = `true`,
		bool	checkCons = `true`
	)

staticinherited

Definition at line 262 of file Games.cpp.

◆ finalize()

virtual bool Game::MP_Param::finalize ( )

inlineprotectedvirtualinherited

Finalize the MP_Param object.

Definition at line 61 of file games.h.

◆ getA()

arma::sp_mat Game::MP_Param::getA ( ) const

inlineinherited

Read-only access to the private variable A.

Definition at line 80 of file games.h.

◆ getB()

arma::sp_mat Game::MP_Param::getB ( ) const

inlineinherited

Read-only access to the private variable B.

Definition at line 83 of file games.h.

◆ getb()

arma::vec Game::MP_Param::getb ( ) const

inlineinherited

Read-only access to the private variable b.

Definition at line 89 of file games.h.

◆ getC()

arma::sp_mat Game::MP_Param::getC ( ) const

inlineinherited

Read-only access to the private variable C.

Definition at line 77 of file games.h.

◆ getc()

arma::vec Game::MP_Param::getc ( ) const

inlineinherited

Read-only access to the private variable c.

Definition at line 86 of file games.h.

◆ getNx()

unsigned int Game::MP_Param::getNx ( ) const

inlineinherited

Read-only access to the private variable Nx.

Definition at line 92 of file games.h.

◆ getNy()

unsigned int Game::MP_Param::getNy ( ) const

inlineinherited

Read-only access to the private variable Ny.

Definition at line 95 of file games.h.

◆ getQ()

arma::sp_mat Game::MP_Param::getQ ( ) const

inlineinherited

Read-only access to the private variable Q.

Definition at line 74 of file games.h.

◆ is_Playable()

bool Game::QP_Param::is_Playable ( const QP_Param & P ) const

inline

Checks if the current object can play a game with another Game::QP_Param object P.

Definition at line 215 of file games.h.

◆ KKT()

unsigned int Game::QP_Param::KKT	(	arma::sp_mat &	M,
		arma::sp_mat &	N,
		arma::vec &	q
	)		const

Compute the KKT conditions for the given QP.

Writes the KKT condition of the parameterized QP As per the convention, y is the decision variable for the QP and that is parameterized in x The KKT conditions are $0 \leq y \perp My + Nx + q \geq 0$

Definition at line 417 of file Games.cpp.

◆ load()

long int Game::QP_Param::load	(	std::string	filename,
		long int	pos = `0`
	)

Loads the Game::QP_Param object stored in a file.

Before calling this function, use the constructor QP_Param::QP_Param(GRBEnv *env) to initialize.

Example usage:

int main()
{
        GRBEnv env;
        Game::QP_Param q1(&env);
        q1.load("./dat/q1data.dat");
        std::cout<<q1<<'\n';
        return 0;
}

Definition at line 529 of file Games.cpp.

◆ make_yQy()

int Game::QP_Param::make_yQy ( )

private

Adds the Gurobi Quadratic objective to the Gurobi model QuadModel.

Definition at line 308 of file Games.cpp.

◆ operator==()

bool Game::QP_Param::operator== ( const QP_Param & Q2 ) const

Definition at line 292 of file Games.cpp.

◆ save()

void Game::QP_Param::save	(	std::string	filename,
		bool	erase = `true`
	)		const

Saves the Game::QP_Param object in a loadable file.

The Game::QP_Param object hence stored can be loaded back using Game::QP_Param::load

Definition at line 514 of file Games.cpp.

◆ set() [1/4]

Game::QP_Param & Game::QP_Param::set	(	const arma::sp_mat &	Q,
		const arma::sp_mat &	C,
		const arma::sp_mat &	A,
		const arma::sp_mat &	B,
		const arma::vec &	c,
		const arma::vec &	b
	)

finalvirtual

Setting the data, while keeping the input objects intact.

Reimplemented from Game::MP_Param.

Definition at line 447 of file Games.cpp.

◆ set() [2/4]

Game::QP_Param & Game::QP_Param::set	(	arma::sp_mat &&	Q,
		arma::sp_mat &&	C,
		arma::sp_mat &&	A,
		arma::sp_mat &&	B,
		arma::vec &&	c,
		arma::vec &&	b
	)

finalvirtual

Faster means to set data. But the input objects might be corrupted now.

Reimplemented from Game::MP_Param.

Definition at line 462 of file Games.cpp.

◆ set() [3/4]

Game::QP_Param & Game::QP_Param::set	(	const QP_objective &	obj,
		const QP_constraints &	cons
	)

finalvirtual

Reimplemented from Game::MP_Param.

Definition at line 485 of file Games.cpp.

◆ set() [4/4]

Game::QP_Param & Game::QP_Param::set	(	QP_objective &&	obj,
		QP_constraints &&	cons
	)

finalvirtual

Setting the data with the inputs being a struct Game::QP_objective and struct Game::QP_constraints

Reimplemented from Game::MP_Param.

Definition at line 477 of file Games.cpp.

◆ setA()

MP_Param& Game::MP_Param::setA ( const arma::sp_mat & A )

inlineinherited

Set the private variable A.

Definition at line 107 of file games.h.

◆ setB()

MP_Param& Game::MP_Param::setB ( const arma::sp_mat & B )

inlineinherited

Set the private variable B.

Definition at line 111 of file games.h.

◆ setb()

MP_Param& Game::MP_Param::setb ( const arma::vec & b )

inlineinherited

Set the private variable b.

Definition at line 119 of file games.h.

◆ setC()

MP_Param& Game::MP_Param::setC ( const arma::sp_mat & C )

inlineinherited

Set the private variable C.

Definition at line 103 of file games.h.

◆ setc()

MP_Param& Game::MP_Param::setc ( const arma::vec & c )

inlineinherited

Set the private variable c.

Definition at line 115 of file games.h.

◆ setQ()

MP_Param& Game::MP_Param::setQ ( const arma::sp_mat & Q )

inlineinherited

Set the private variable Q.

Definition at line 99 of file games.h.

◆ size()

unsigned int Game::MP_Param::size ( )

protectedinherited

Calculates Nx, Ny and Ncons Computes parameters in MP_Param:

Computes Ny as number of rows in MP_Param::Q
Computes Nx as number of columns in MP_Param::C

Computes Ncons as number of rows in MP_Param::b, i.e., the RHS of the constraints

For proper working, MP_Param::dataCheck() has to be run after this.
@returns @p Ny, Number of variables in the quadratic program, QP

Definition at line 159 of file Games.cpp.

◆ solveFixed()

unique_ptr< GRBModel > Game::QP_Param::solveFixed ( arma::vec x )

Given a value for the parameters $x$ in the definition of QP_Param, solve the parameterized quadratic program to optimality.

In terms of game theory, this can be viewed as the best response for a set of decisions by other players.

Exceptions

GRBException if argument vector size is not

compatible with the Game::QP_Param definition.

Parameters

x	Other players' decisions

Definition at line 331 of file Games.cpp.

◆ write()

void Game::QP_Param::write	(	std::string	filename,
		bool	append
	)		const

Writes a given parameterized Mathematical program to a set of files.

Definition at line 86 of file Games.cpp.

Field Documentation

◆ A

arma::sp_mat Game::MP_Param::A

protectedinherited

Definition at line 55 of file games.h.

◆ B

arma::sp_mat Game::MP_Param::B

protectedinherited

Definition at line 55 of file games.h.

◆ b

arma::vec Game::MP_Param::b

protectedinherited

Definition at line 56 of file games.h.

◆ C

arma::sp_mat Game::MP_Param::C

protectedinherited

Definition at line 55 of file games.h.

◆ c

arma::vec Game::MP_Param::c

protectedinherited

Definition at line 56 of file games.h.

◆ env

GRBEnv* Game::QP_Param::env

private

Definition at line 161 of file games.h.

◆ made_yQy

bool Game::QP_Param::made_yQy

private

Definition at line 163 of file games.h.

◆ Ncons

unsigned int Game::MP_Param::Ncons

protectedinherited

Definition at line 58 of file games.h.

◆ Nx

unsigned int Game::MP_Param::Nx

protectedinherited

Definition at line 58 of file games.h.

◆ Ny

unsigned int Game::MP_Param::Ny

protectedinherited

Definition at line 58 of file games.h.

◆ Q

arma::sp_mat Game::MP_Param::Q

protectedinherited

Definition at line 55 of file games.h.

◆ QuadModel

GRBModel Game::QP_Param::QuadModel

private

Definition at line 162 of file games.h.

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

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ QP_Param() [1/3]

◆ QP_Param() [2/3]

◆ QP_Param() [3/3]

Member Function Documentation

◆ addDummy()

◆ bound()

◆ computeObjective()

◆ dataCheck() [1/2]

◆ dataCheck() [2/2]

◆ finalize()

◆ getA()

◆ getB()

◆ getb()

◆ getC()

◆ getc()

◆ getNx()

◆ getNy()

◆ getQ()

◆ is_Playable()

◆ KKT()

◆ load()

◆ make_yQy()

◆ operator==()

◆ save()

◆ set() [1/4]

◆ set() [2/4]

◆ set() [3/4]

◆ set() [4/4]

◆ setA()

◆ setB()

◆ setb()

◆ setC()

◆ setc()

◆ setQ()

◆ size()

◆ solveFixed()

◆ write()

Field Documentation

◆ A

◆ B

◆ b

◆ C

◆ c

◆ env

◆ made_yQy

◆ Ncons

◆ Nx

◆ Ny

◆ Q

◆ QuadModel