Express the Primal-Dual Interior Point gradient as an equality constraint. More...

#include <ROL_InteriorPointPrimalDualResidual.hpp>

Inheritance diagram for ROL::InteriorPoint::PrimalDualResidual< Real >:

Public Member Functions
	PrimalDualResidual (const ROL::Ptr< OBJ > &obj, const ROL::Ptr< CON > &eqcon, const ROL::Ptr< CON > &incon, const V &x)

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	updatePenalty (Real mu)

	PrimalDualResidual (const ROL::Ptr< OBJ > &obj, const ROL::Ptr< CON > &eqcon, const ROL::Ptr< CON > &incon, const V &x)

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	updatePenalty (Real mu)

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

	Constraint (void)

virtual void	update (const Vector< Real > &x, UpdateType type, int iter=-1)
	Update constraint function. More...

virtual 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...

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 Vector< Real >	V

typedef PartitionedVector< Real >	PV

typedef Objective< Real >	OBJ

typedef Constraint< Real >	CON

typedef PV::size_type	size_type

typedef Vector< Real >	V

typedef PartitionedVector< Real >	PV

typedef Objective< Real >	OBJ

typedef Constraint< Real >	CON

typedef PV::size_type	size_type

Private Attributes
ROL::Ptr< OBJ >	obj_

ROL::Ptr< CON >	eqcon_

ROL::Ptr< CON >	incon_

ROL::Ptr< V >	qo_

ROL::Ptr< V >	qs_

ROL::Ptr< V >	qe_

ROL::Ptr< V >	qi_

Real	mu_

ROL::Ptr< LinearOperator< Real > >	sym_

Static Private Attributes
static const size_type	OPT = 0

static const size_type	SLACK = 1

static const size_type	EQUAL = 2

static const size_type	INEQ = 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::InteriorPoint::PrimalDualResidual< Real >

Express the Primal-Dual Interior Point gradient as an equality constraint.

     See Nocedal & Wright second edition equation (19.6)
     In that book the convention for naming components

     x - optimization variable (here subscript o)
     s - slack variable (here subscript s)
     y - Lagrange multiplier for the equality constraint (here subscript e)
     z - Lagrange multiplier for the inequality constraint (here subscript i)

Definition at line 42 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

Member Typedef Documentation

template<class Real >

typedef Vector<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::V

private

Definition at line 45 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef PartitionedVector<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::PV

private

Definition at line 46 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef Objective<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::OBJ

private

Definition at line 47 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef Constraint<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::CON

private

Definition at line 48 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef PV::size_type ROL::InteriorPoint::PrimalDualResidual< Real >::size_type

private

Definition at line 51 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef Vector<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::V

private

Definition at line 45 of file ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef PartitionedVector<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::PV

private

Definition at line 46 of file ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef Objective<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::OBJ

private

Definition at line 47 of file ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef Constraint<Real> ROL::InteriorPoint::PrimalDualResidual< Real >::CON

private

Definition at line 48 of file ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

typedef PV::size_type ROL::InteriorPoint::PrimalDualResidual< Real >::size_type

private

Definition at line 51 of file ROL_InteriorPointPrimalDualResidual.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::InteriorPoint::PrimalDualResidual< Real >::PrimalDualResidual	(	const ROL::Ptr< OBJ > &	obj,
		const ROL::Ptr< CON > &	eqcon,
		const ROL::Ptr< CON > &	incon,
		const V &	x
	)

inline

Definition at line 75 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

ROL::InteriorPoint::PrimalDualResidual< Real >::PrimalDualResidual	(	const ROL::Ptr< OBJ > &	obj,
		const ROL::Ptr< CON > &	eqcon,
		const ROL::Ptr< CON > &	incon,
		const V &	x
	)

inline

Definition at line 75 of file ROL_InteriorPointPrimalDualResidual.hpp.

Member Function Documentation

template<class Real >

void ROL::InteriorPoint::PrimalDualResidual< 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 93 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

void ROL::InteriorPoint::PrimalDualResidual< 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#91, 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 147 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

void ROL::InteriorPoint::PrimalDualResidual< Real >::updatePenalty ( Real mu )

inline

Definition at line 222 of file interiorpoint/ROL_InteriorPointPrimalDualResidual.hpp.

References ROL::InteriorPoint::PrimalDualResidual< Real >::mu_.

template<class Real >

void ROL::InteriorPoint::PrimalDualResidual< 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 93 of file ROL_InteriorPointPrimalDualResidual.hpp.

template<class Real >

void ROL::InteriorPoint::PrimalDualResidual< 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#91, 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 147 of file ROL_InteriorPointPrimalDualResidual.hpp.