Symmetrized form of the KKT operator for the Type-EB problem with equality and bound multipliers. More...

#include <ROL_PrimalDualInteriorPointReducedResidual.hpp>

Inheritance diagram for ROL::PrimalDualInteriorPointResidual< Real >:

Classes
class	InFill

class	SafeDivide

class	SetZeros

Public Member Functions
	PrimalDualInteriorPointResidual (const ROL::Ptr< PENALTY > &penalty, const ROL::Ptr< CON > &con, const V &x, ROL::Ptr< V > &scratch)

void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count. More...

void	value (V &c, const V &x, Real &tol)
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More...

void	applyJacobian (V &jv, const V &v, const V &x, Real &tol)
	Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\). More...

int	getNumberFunctionEvaluations (void) const

int	getNumberGradientEvaluations (void) const

int	getNumberConstraintEvaluations (void) const

	PrimalDualInteriorPointResidual (const ROL::Ptr< OBJ > &obj, const ROL::Ptr< CON > &con, const ROL::Ptr< BND > &bnd, const V &x, const ROL::Ptr< const V > &maskL, const ROL::Ptr< const V > &maskU, ROL::Ptr< V > &scratch, Real mu, bool symmetrize)

void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count. More...

void	value (V &c, const V &x, Real &tol)
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More...

void	applyJacobian (V &jv, const V &v, const V &x, Real &tol)
	Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\). More...

void	reset (const Real mu)

int	getNumberFunctionEvaluations (void) const

int	getNumberGradientEvaluations (void) const

int	getNumberConstraintEvaluations (void) const

Public Member Functions inherited from ROL::Constraint< Real >
virtual	~Constraint (void)

	Constraint (void)

virtual void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^, \mathcal{X}^)\), to vector \(v\). More...

virtual void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualv, Real &tol)
	Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^, \mathcal{X}^)\), to vector \(v\). More...

virtual void	applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \). More...

virtual std::vector< Real >	solveAugmentedSystem (Vector< Real > &v1, Vector< Real > &v2, const Vector< Real > &b1, const Vector< Real > &b2, const Vector< Real > &x, Real &tol)
	Approximately solves the augmented system \[ \begin{pmatrix} I & c'(x)^* \\ c'(x) & 0 \end{pmatrix} \begin{pmatrix} v_{1} \\ v_{2} \end{pmatrix} = \begin{pmatrix} b_{1} \\ b_{2} \end{pmatrix} \] where \(v_{1} \in \mathcal{X}\), \(v_{2} \in \mathcal{C}^\), \(b_{1} \in \mathcal{X}^\), \(b_{2} \in \mathcal{C}\), \(I : \mathcal{X} \rightarrow \mathcal{X}^\) is an identity or Riesz operator, and \(0 : \mathcal{C}^ \rightarrow \mathcal{C}\) is a zero operator. More...

virtual void	applyPreconditioner (Vector< Real > &pv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g, Real &tol)
	Apply a constraint preconditioner at \(x\), \(P(x) \in L(\mathcal{C}, \mathcal{C}^)\), to vector \(v\). Ideally, this preconditioner satisfies the following relationship: \[ \left[c'(x) \circ R \circ c'(x)^ \circ P(x)\right] v = v \,, \] where R is the appropriate Riesz map in \(L(\mathcal{X}^*, \mathcal{X})\). It is used by the solveAugmentedSystem method. More...

void	activate (void)
	Turn on constraints. More...

void	deactivate (void)
	Turn off constraints. More...

bool	isActivated (void)
	Check if constraints are on. More...

virtual std::vector < std::vector< Real > >	checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference check for the constraint Jacobian application. More...

virtual std::vector < std::vector< Real > >	checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference check for the constraint Jacobian application. More...

virtual std::vector < std::vector< Real > >	checkApplyAdjointJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &c, const Vector< Real > &ajv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS)
	Finite-difference check for the application of the adjoint of constraint Jacobian. More...

virtual Real	checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const bool printToStream=true, std::ostream &outStream=std::cout)

virtual Real	checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualw, const Vector< Real > &dualv, const bool printToStream=true, std::ostream &outStream=std::cout)

virtual std::vector < std::vector< Real > >	checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const std::vector< Real > &step, const bool printToScreen=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference check for the application of the adjoint of constraint Hessian. More...

virtual std::vector < std::vector< Real > >	checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const bool printToScreen=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference check for the application of the adjoint of constraint Hessian. More...

virtual void	setParameter (const std::vector< Real > &param)

Private Types
typedef ROL::ParameterList	PL

typedef Vector< Real >	V

typedef PartitionedVector< Real >	PV

typedef Objective< Real >	OBJ

typedef Constraint< Real >	CON

typedef BoundConstraint< Real >	BND

typedef LinearOperator< Real >	LOP

typedef InteriorPointPenalty < Real >	PENALTY

typedef Elementwise::ValueSet < Real >	ValueSet

typedef PV::size_type	size_type

typedef ROL::ParameterList	PL

typedef Vector< Real >	V

typedef PartitionedVector< Real >	PV

typedef Objective< Real >	OBJ

typedef Constraint< Real >	CON

typedef BoundConstraint< Real >	BND

typedef Elementwise::ValueSet < Real >	ValueSet

typedef PV::size_type	size_type

Private Member Functions
ROL::Ptr< V >	getOptMult (V &vec)

ROL::Ptr< const V >	getOptMult (const V &vec)

Private Attributes
ROL::Ptr< const V >	x_

ROL::Ptr< const V >	l_

ROL::Ptr< const V >	zl_

ROL::Ptr< const V >	zu_

ROL::Ptr< const V >	xl_

ROL::Ptr< const V >	xu_

const ROL::Ptr< const V >	maskL_

const ROL::Ptr< const V >	maskU_

ROL::Ptr< V >	scratch_

const ROL::Ptr< PENALTY >	penalty_

const ROL::Ptr< OBJ >	obj_

const ROL::Ptr< CON >	con_

const ROL::Ptr< BND >	bnd_

Real	mu_

bool	symmetrize_

Real	one_

Real	zero_

int	nfval_

int	ngrad_

int	ncval_

Elementwise::Multiply< Real >	mult_

SafeDivide	div_

SetZeros	setZeros_

InFill	inFill_

Static Private Attributes
static const size_type	OPT = 0

static const size_type	EQUAL = 1

static const size_type	LOWER = 2

static const size_type	UPPER = 3

Additional Inherited Members
Protected Member Functions inherited from ROL::Constraint< Real >
const std::vector< Real >	getParameter (void) const

Detailed Description

template<class Real>
class ROL::PrimalDualInteriorPointResidual< Real >

Symmetrized form of the KKT operator for the Type-EB problem with equality and bound multipliers.

The system is symmetrized by multiplying through by

S = [ I 0 0 0 ] [ 0 I 0 0 ] [ 0 0 -inv(Zl) 0 ] [ 0 0 0 -inv(Zu) ]

Where Zl and Zu are diagonal matrices containing the lower and upper bound multipliers respectively

Infinite bounds have identically zero-valued lagrange multipliers.

Definition at line 111 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

Member Typedef Documentation

template<class Real >

typedef ROL::ParameterList ROL::PrimalDualInteriorPointResidual< Real >::PL

private

Definition at line 113 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef Vector<Real> ROL::PrimalDualInteriorPointResidual< Real >::V

private

Definition at line 115 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef PartitionedVector<Real> ROL::PrimalDualInteriorPointResidual< Real >::PV

private

Definition at line 116 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef Objective<Real> ROL::PrimalDualInteriorPointResidual< Real >::OBJ

private

Definition at line 117 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef Constraint<Real> ROL::PrimalDualInteriorPointResidual< Real >::CON

private

Definition at line 118 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef BoundConstraint<Real> ROL::PrimalDualInteriorPointResidual< Real >::BND

private

Definition at line 119 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef LinearOperator<Real> ROL::PrimalDualInteriorPointResidual< Real >::LOP

private

Definition at line 120 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef InteriorPointPenalty<Real> ROL::PrimalDualInteriorPointResidual< Real >::PENALTY

private

Definition at line 121 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef Elementwise::ValueSet<Real> ROL::PrimalDualInteriorPointResidual< Real >::ValueSet

private

Definition at line 123 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef PV::size_type ROL::PrimalDualInteriorPointResidual< Real >::size_type

private

Definition at line 125 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

typedef ROL::ParameterList ROL::PrimalDualInteriorPointResidual< Real >::PL

private

Definition at line 80 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef Vector<Real> ROL::PrimalDualInteriorPointResidual< Real >::V

private

Definition at line 82 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef PartitionedVector<Real> ROL::PrimalDualInteriorPointResidual< Real >::PV

private

Definition at line 83 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef Objective<Real> ROL::PrimalDualInteriorPointResidual< Real >::OBJ

private

Definition at line 84 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef Constraint<Real> ROL::PrimalDualInteriorPointResidual< Real >::CON

private

Definition at line 85 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef BoundConstraint<Real> ROL::PrimalDualInteriorPointResidual< Real >::BND

private

Definition at line 86 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef Elementwise::ValueSet<Real> ROL::PrimalDualInteriorPointResidual< Real >::ValueSet

private

Definition at line 88 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

typedef PV::size_type ROL::PrimalDualInteriorPointResidual< Real >::size_type

private

Definition at line 90 of file ROL_PrimalDualInteriorPointResidual.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::PrimalDualInteriorPointResidual< Real >::PrimalDualInteriorPointResidual	(	const ROL::Ptr< PENALTY > &	penalty,
		const ROL::Ptr< CON > &	con,
		const V &	x,
		ROL::Ptr< V > &	scratch
	)

inline

Definition at line 154 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

ROL::PrimalDualInteriorPointResidual< Real >::PrimalDualInteriorPointResidual	(	const ROL::Ptr< OBJ > &	obj,
		const ROL::Ptr< CON > &	con,
		const ROL::Ptr< BND > &	bnd,
		const V &	x,
		const ROL::Ptr< const V > &	maskL,
		const ROL::Ptr< const V > &	maskU,
		ROL::Ptr< V > &	scratch,
		Real	mu,
		bool	symmetrize
	)

inline

Definition at line 176 of file ROL_PrimalDualInteriorPointResidual.hpp.

References ROL::PrimalDualInteriorPointResidual< Real >::EQUAL, ROL::PartitionedVector< Real >::get(), ROL::PrimalDualInteriorPointResidual< Real >::l_, ROL::PrimalDualInteriorPointResidual< Real >::LOWER, ROL::PrimalDualInteriorPointResidual< Real >::OPT, ROL::PrimalDualInteriorPointResidual< Real >::UPPER, ROL::PrimalDualInteriorPointResidual< Real >::x_, ROL::PrimalDualInteriorPointResidual< Real >::zl_, and ROL::PrimalDualInteriorPointResidual< Real >::zu_.

Member Function Documentation

template<class Real >

void ROL::PrimalDualInteriorPointResidual< Real >::update	(	const Vector< Real > &	x,
		bool	flag = `true`,
		int	iter = `-1`
	)

inlinevirtual

Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count.

Reimplemented from ROL::Constraint< Real >.

Definition at line 180 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

void ROL::PrimalDualInteriorPointResidual< Real >::value	(	V &	c,
		const V &	x,
		Real &	tol
	)

inlinevirtual

Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\).

Parameters

[out]	c	is the result of evaluating the constraint operator at x; a constraint-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \(\mathsf{c} = c(x)\), where \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).

Implements ROL::Constraint< Real >.

Definition at line 196 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

void ROL::PrimalDualInteriorPointResidual< Real >::applyJacobian	(	V &	jv,
		const V &	v,
		const V &	x,
		Real &	tol
	)

inlinevirtual

Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\).

  @param[out]      jv  is the result of applying the constraint Jacobian to @b v at @b x; a constraint-space vector
  @param[in]       v   is an optimization-space vector
  @param[in]       x   is the constraint argument; an optimization-space vector
  @param[in,out]   tol is a tolerance for inexact evaluations; currently unused

  On return, \form#77, where

\(v \in \mathcal{X}\), \(\mathsf{jv} \in \mathcal{C}\).

The default implementation is a finite-difference approximation.

Reimplemented from ROL::Constraint< Real >.

Definition at line 221 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

template<class Real >

int ROL::PrimalDualInteriorPointResidual< Real >::getNumberFunctionEvaluations ( void ) const

inline

Definition at line 282 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

References ROL::PrimalDualInteriorPointResidual< Real >::nfval_.

template<class Real >

int ROL::PrimalDualInteriorPointResidual< Real >::getNumberGradientEvaluations ( void ) const

inline

Definition at line 286 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

References ROL::PrimalDualInteriorPointResidual< Real >::ngrad_.

template<class Real >

int ROL::PrimalDualInteriorPointResidual< Real >::getNumberConstraintEvaluations ( void ) const

inline

Definition at line 290 of file ROL_PrimalDualInteriorPointReducedResidual.hpp.

References ROL::PrimalDualInteriorPointResidual< Real >::ncval_.

template<class Real >

ROL::Ptr<V> ROL::PrimalDualInteriorPointResidual< Real >::getOptMult ( V & vec )

inlineprivate

Definition at line 158 of file ROL_PrimalDualInteriorPointResidual.hpp.

References ROL::PrimalDualInteriorPointResidual< Real >::EQUAL, ROL::PartitionedVector< Real >::get(), and ROL::PrimalDualInteriorPointResidual< Real >::OPT.

template<class Real >

ROL::Ptr<const V> ROL::PrimalDualInteriorPointResidual< Real >::getOptMult ( const V & vec )

inlineprivate

Definition at line 165 of file ROL_PrimalDualInteriorPointResidual.hpp.

References ROL::PrimalDualInteriorPointResidual< Real >::EQUAL, ROL::PartitionedVector< Real >::get(), and ROL::PrimalDualInteriorPointResidual< Real >::OPT.

template<class Real >

void ROL::PrimalDualInteriorPointResidual< Real >::update	(	const Vector< Real > &	x,
		bool	flag = `true`,
		int	iter = `-1`
	)

inlinevirtual

Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count.

Reimplemented from ROL::Constraint< Real >.

Definition at line 200 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

void ROL::PrimalDualInteriorPointResidual< Real >::value	(	V &	c,
		const V &	x,
		Real &	tol
	)

inlinevirtual

Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\).

Parameters

[out]	c	is the result of evaluating the constraint operator at x; a constraint-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \(\mathsf{c} = c(x)\), where \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).

Implements ROL::Constraint< Real >.

Definition at line 217 of file ROL_PrimalDualInteriorPointResidual.hpp.

template<class Real >

void ROL::PrimalDualInteriorPointResidual< Real >::applyJacobian	(	V &	jv,
		const V &	v,
		const V &	x,
		Real &	tol
	)

inlinevirtual

Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\).

  @param[out]      jv  is the result of applying the constraint Jacobian to @b v at @b x; a constraint-space vector
  @param[in]       v   is an optimization-space vector
  @param[in]       x   is the constraint argument; an optimization-space vector
  @param[in,out]   tol is a tolerance for inexact evaluations; currently unused

  On return, \form#77, where

\(v \in \mathcal{X}\), \(\mathsf{jv} \in \mathcal{C}\).

The default implementation is a finite-difference approximation.

Reimplemented from ROL::Constraint< Real >.

Definition at line 314 of file ROL_PrimalDualInteriorPointResidual.hpp.